Bitcoin Analysis and Visualization with Plotly, Price Prediction with Keras.ipynb

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  {
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   "metadata": {},
   "source": [
    "## Bitcoin Analysis and Visualization with Plotly, Price Prediction with LSTM model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\* In order to see fully rendered visualizations by Plotly in jupyter notebook, please visit [this link](https://nbviewer.jupyter.org/github/AsunaMasuda/Bitcoin_plotly_keras/tree/master/Bitcoin%20Analysis%20and%20Visualization%20with%20Plotly,%20Price%20Prediction%20with%20Keras.ipynb) on jupyter nbviewer. (ipython files in Github repository cannot show visualizations by plotly.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overview of this notebook\n",
    "This notebook focuses on these two aspects below, mainly for the writer's self-learning purpose:\n",
    "\n",
    "- Data clearning and analysis with Python libraries and Bitcoin price prediction by deep learning algolism called LSTM with Keras\n",
    "- Interactive Data visualizations with Plotly\n",
    "\n",
    "To create this notebook, \n",
    "<br>For data visualization with Plotly:\n",
    "<br>I refered to [a Kaggle post](https://www.kaggle.com/kanncaa1/plotly-tutorial-for-beginners) by [DATAI](https://www.kaggle.com/kanncaa1) and Plotly [official document](https://plot.ly/python/).\n",
    "<br>For price prediction with LSTM by Keras:\n",
    "<br>I refered to [a jupyter notebook](https://github.com/dashee87/blogScripts/blob/master/Jupyter/2017-11-20-predicting-cryptocurrency-prices-with-deep-learning.ipynb) which explained an applicaiton of deep learning to Bitcoin/Etherium price prediction by a data scientist [David Sheeran](https://dashee87.github.io/about/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><img src=\"bit_image.jpg\" style=\"width:500px\"></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Context\n",
    "\n",
    "Bitcoin is the longest running and most well known cryptocurrency, first released as open source in 2009 by the anonymous Satoshi Nakamoto. Bitcoin serves as a decentralized medium of digital exchange, with transactions verified and recorded in a public distributed ledger (the blockchain) without the need for a trusted record keeping authority or central intermediary. Transaction blocks contain a SHA-256 cryptographic hash of previous transaction blocks, and are thus \"chained\" together, serving as an immutable record of all transactions that have ever occurred. As with any currency/commodity on the market, bitcoin trading and financial instruments soon followed public adoption of bitcoin and continue to grow. Included here is historical bitcoin market data at 1-min intervals for select bitcoin exchanges where trading takes place."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Datasets\n",
    "- coinbaseUSD_1-min_data_2014-12-01_to_2019-01-09.csv\n",
    "- bitstampUSD_1-min_data_2012-01-01_to_2019-08-12.csv\n",
    "\n",
    "CSV files for select bitcoin exchanges for the time period of Jan 2012 to August 2019, with minute to minute updates of OHLC (Open, High, Low, Close), Volume in BTC and indicated currency, and weighted bitcoin price. Timestamps are in Unix time. Timestamps without any trades or activity have their data fields filled with NaNs. If a timestamp is missing, or if there are jumps, this may be because the exchange (or its API) was down, the exchange (or its API) did not exist, or some other unforseen technical error in data reporting or gathering. All effort has been made to deduplicate entries and verify the contents are correct and complete to the best of my ability, but obviously trust at your own risk."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explanation of the columns:\n",
    "- Timestamp: Start time of time window (60s window), in Unix time\n",
    "- OpenOpen: price at start time window\n",
    "- High: High price within time window\n",
    "- Low: Low price within time window\n",
    "- Close: Close price at end of time window\n",
    "- Volume_(BTC): Amount of BTC transacted in time window\n",
    "- Volume_(Currency): Amount of Currency transacted in time window\n",
    "- Weighted_Price: Volume-Weighted Average Price price (VWAP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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       "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
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       "        require.undef(\"plotly\");\n",
       "        requirejs.config({\n",
       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
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       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
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       "        }\n",
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   "source": [
    "# import libraries\n",
    "import time\n",
    "start_time=time.time()\n",
    "import numpy as np\n",
    "from collections import Counter\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from plotly import __version__\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "import plotly as py\n",
    "import plotly.graph_objs as go\n",
    "init_notebook_mode(connected=True)\n",
    "plt.rcParams['figure.figsize']=(12,5)\n",
    "import numpy as np\n",
    "import operator\n",
    "import pandas as pd\n",
    "\n",
    "# not to show warning messages\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read csv files\n",
    "df_bitstamp = pd.read_csv('bitstampUSD_1-min_data_2012-01-01_to_2019-08-12.csv')\n",
    "df_coinbase = pd.read_csv('coinbaseUSD_1-min_data_2014-12-01_to_2019-01-09.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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       "    Timestamp  Open  High   Low  Close  Volume_(BTC)  Volume_(Currency)  \\\n",
       "0  1325317920  4.39  4.39  4.39   4.39      0.455581                2.0   \n",
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       "4  1325318160   NaN   NaN   NaN    NaN           NaN                NaN   \n",
       "\n",
       "   Weighted_Price  \n",
       "0            4.39  \n",
       "1             NaN  \n",
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       "3             NaN  \n",
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df_bitstamp.head()"
   ]
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   "cell_type": "code",
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   "metadata": {
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   "outputs": [
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     "execution_count": 4,
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   "source": [
    "df_bitstamp.shape"
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       "    Timestamp   Open   High    Low  Close  Volume_(BTC)  Volume_(Currency)  \\\n",
       "0  1417411980  300.0  300.0  300.0  300.0          0.01                3.0   \n",
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       "\n",
       "   Weighted_Price  \n",
       "0           300.0  \n",
       "1             NaN  \n",
       "2             NaN  \n",
       "3             NaN  \n",
       "4             NaN  "
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_coinbase.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
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     "execution_count": 6,
     "metadata": {},
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   "source": [
    "df_coinbase.shape"
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  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert Timestamp from unix\n",
    "df_bitstamp = pd.concat([df_bitstamp.drop('Timestamp', axis=1),\n",
    "                         pd.DataFrame(pd.to_datetime(df_bitstamp['Timestamp'], unit='s'))], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_bitstamp.index = df_bitstamp.Timestamp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert Timestamp from unix\n",
    "df_coinbase = pd.concat([df_coinbase.drop('Timestamp', axis=1), \n",
    "                         pd.DataFrame(pd.to_datetime(df_coinbase['Timestamp'], unit='s'))], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_coinbase.index = df_coinbase.Timestamp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check null percentages in both datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create dataframes that hold missing values\n",
    "bitstamp_missing = df_bitstamp.isnull().mean()*100\n",
    "coinbase_missing = df_coinbase.isnull().mean()*100"
   ]
  },
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   "execution_count": 12,
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\"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"Null Percentages\"}, \"width\": 800, \"xaxis\": {\"anchor\": \"y\", \"domain\": [0.0, 0.45]}, \"xaxis2\": {\"anchor\": \"y2\", \"domain\": [0.55, 1.0]}, \"yaxis\": {\"anchor\": \"x\", \"domain\": [0.0, 1.0]}, \"yaxis2\": {\"anchor\": \"x2\", \"domain\": [0.0, 1.0]}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('262bc597-3102-41c6-a51e-00a2b6543b18');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import graph objects as \"go\"\n",
    "import plotly.graph_objs as go\n",
    "from plotly import subplots\n",
    "\n",
    "# Draw graphes\n",
    "trace0 = go.Bar(x = bitstamp_missing.index,\n",
    "               y = bitstamp_missing,\n",
    "               marker = dict(color = 'rgba(245, 140, 130, 0.5)',\n",
    "               line=dict(color='rgb(0,0,0)',width=1.5)))\n",
    "\n",
    "trace1 = go.Bar(x = coinbase_missing.index,\n",
    "               y = coinbase_missing,\n",
    "               marker = dict(color = 'rgba(130, 135, 245, 0.5)',\n",
    "               line=dict(color='rgb(0,0,0)',width=1.5)))\n",
    "\n",
    "fig = subplots.make_subplots(rows=1, cols=2,subplot_titles=(\"bitstamp dataframe\",\"coinbase dataframe\"))\n",
    "\n",
    "fig.append_trace(trace0, 1, 1)\n",
    "fig.append_trace(trace1, 1, 2)\n",
    "\n",
    "fig['layout'].update(height=400, width=800, title='Null Percentages')\n",
    "iplot(fig);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems all columns except Timestamp have missing values at the same rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Since the timestamp is not empty, we fill missing value with ffill method\n",
    "df_bitstamp['Open'].fillna(method='ffill', inplace=True)\n",
    "df_bitstamp['High'].fillna(method='ffill', inplace=True)\n",
    "df_bitstamp['Low'].fillna(method='ffill', inplace=True)\n",
    "df_bitstamp['Close'].fillna(method='ffill', inplace=True)\n",
    "df_bitstamp['Volume_(BTC)'].fillna(method='ffill', inplace=True)\n",
    "df_bitstamp['Volume_(Currency)'].fillna(method='ffill', inplace=True)\n",
    "df_bitstamp['Weighted_Price'].fillna(method='ffill', inplace=True)\n",
    "\n",
    "df_coinbase['Open'].fillna(method='ffill', inplace=True)\n",
    "df_coinbase['High'].fillna(method='ffill', inplace=True)\n",
    "df_coinbase['Low'].fillna(method='ffill', inplace=True)\n",
    "df_coinbase['Close'].fillna(method='ffill', inplace=True)\n",
    "df_coinbase['Volume_(BTC)'].fillna(method='ffill', inplace=True)\n",
    "df_coinbase['Volume_(Currency)'].fillna(method='ffill', inplace=True)\n",
    "df_coinbase['Weighted_Price'].fillna(method='ffill', inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Price change with timeseries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# draw graphs of daily Close prices of both datasets  \n",
    "plt.plot(df_bitstamp.index, df_bitstamp.Close, alpha=0.5, color='blue')\n",
    "plt.plot(df_coinbase.index, df_coinbase.Close, alpha=0.5, color='orange')\n",
    "plt.xlabel('time', fontsize=12)\n",
    "plt.ylabel('price /USD', fontsize=12);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- coinbase data is missing before 2015 and after 2019\n",
    "- There was a peak in price between late 2017 and middle of 2018\n",
    "\n",
    "bitstamp data seems to have more comprehensive data than coinbase data, so I'll be using only bitstamp data for further analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More insights on bitstamp data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change timeseries to monthly and weekly\n",
    "df_bitstamp_m = df_bitstamp.resample('M').mean()\n",
    "df_bitstamp_w = df_bitstamp.resample('W').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "config": {
        "linkText": "Export to plot.ly",
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          "color": "rgba(235, 115, 150, 0.8)"
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         "mode": "lines",
         "name": "Weekly",
         "type": "scatter",
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       "            </script>\n",
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# vizualize monthly and weekly roundad Close price\n",
    "trace_week = go.Scatter(x = df_bitstamp_w.index,\n",
    "                   y = df_bitstamp_w.Close,\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Weekly\",\n",
    "                   marker = dict(color = 'rgba(235, 115, 150, 0.8)')\n",
    "                       )\n",
    "trace_month = go.Scatter(x = df_bitstamp_m.index,\n",
    "                   y = df_bitstamp_m.Close,\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Monthly\",\n",
    "                   marker = dict(color = 'rgba(115, 120, 235, 0.8)')\n",
    "                       )\n",
    "\n",
    "data_2 = [trace_week, trace_month]\n",
    "\n",
    "\n",
    "updatemenus = list([\n",
    "    dict(active=-1,\n",
    "         buttons=list([\n",
    "            dict(label = 'Weekly',\n",
    "                 method = 'update',\n",
    "                 args = [{'visible': [True, False]}\n",
    "                         ]),\n",
    "            dict(label = 'Monthly',\n",
    "                 method = 'update',\n",
    "                 args = [{'visible': [False, True]}\n",
    "                         ]),\n",
    "            dict(label = 'Reset',\n",
    "                 method = 'update',\n",
    "                 args = [{'visible': [True, True]}])\n",
    "         ]),\n",
    "         x = 1.28, y = 0.75),\n",
    "])\n",
    "\n",
    "layout_2 = go.Layout(height=400, width=550,\n",
    "                title='Weekly/Monthly Close Price', \n",
    "                xaxis_title=\"timestamp\",\n",
    "                yaxis_title=\"VWAP /USD\",\n",
    "                updatemenus=updatemenus)\n",
    "\n",
    "fig = dict(data = data_2, layout = layout_2)\n",
    "iplot(fig);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('409204c8-b27c-459f-8f58-229b9c021317');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the other data, Volume_(BTC), Volume_(Currency), \n",
    "# Weighted_Price, in monthly basis\n",
    "\n",
    "trace_btc = go.Scatter(x = df_bitstamp_m.index,\n",
    "                   y = df_bitstamp_w['Volume_(BTC)'],\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Volume_(BTC)\",\n",
    "                   marker = dict(color = 'rgba(235, 115, 150, 0.8)')\n",
    "                       )\n",
    "trace_currency = go.Scatter(x = df_bitstamp_m.index,\n",
    "                   y = df_bitstamp_m['Volume_(Currency)'],\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Volume_(Currency)\",\n",
    "                   marker = dict(color = 'rgba(115, 120, 235, 0.8)')\n",
    "                       )\n",
    "trace_weighted_price = go.Scatter(x = df_bitstamp_m.index,\n",
    "                   y = df_bitstamp_m['Weighted_Price'],\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Weighted_Price\",\n",
    "                   marker = dict(color = 'rgba(245, 170, 60, 0.8)')\n",
    "                       )\n",
    "\n",
    "fig = subplots.make_subplots(rows=3, cols=1,\n",
    "                             subplot_titles=(\"Volume_(BTC)\",\"Volume_(Currency)\", \"Weighted_Price\"))\n",
    "\n",
    "fig.append_trace(trace_btc, 1, 1)\n",
    "fig.append_trace(trace_currency, 2, 1)\n",
    "fig.append_trace(trace_weighted_price, 3, 1)\n",
    "\n",
    "fig['layout'].update(height=650, width=750, showlegend=False)\n",
    "\n",
    "iplot(fig);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Seasonal Trend Decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1224x864 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define seasonal trend decomposition\n",
    "from statsmodels.tsa.seasonal import seasonal_decompose\n",
    "\n",
    "def decompose(series):\n",
    "    plt.figure(figsize = (17,12))\n",
    "    seasonal_decompose(series).plot()\n",
    "    plt.show()\n",
    "\n",
    "decompose(df_bitstamp_m.Weighted_Price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Price prediction with random walks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change timeseries to daily\n",
    "df_bitstamp = df_bitstamp.resample('D').mean()\n",
    "df_bitstamp = df_bitstamp.reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Timestamp</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume_(BTC)</th>\n",
       "      <th>Volume_(Currency)</th>\n",
       "      <th>Weighted_Price</th>\n",
       "      <th>day_diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2011-12-31</td>\n",
       "      <td>4.472552</td>\n",
       "      <td>4.472624</td>\n",
       "      <td>4.472552</td>\n",
       "      <td>4.472624</td>\n",
       "      <td>7.590527</td>\n",
       "      <td>34.069690</td>\n",
       "      <td>4.472579</td>\n",
       "      <td>0.000016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2012-01-01</td>\n",
       "      <td>4.680778</td>\n",
       "      <td>4.680778</td>\n",
       "      <td>4.680778</td>\n",
       "      <td>4.680778</td>\n",
       "      <td>5.861697</td>\n",
       "      <td>27.856539</td>\n",
       "      <td>4.680778</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2012-01-02</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>11.566478</td>\n",
       "      <td>57.832389</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2012-01-03</td>\n",
       "      <td>5.145917</td>\n",
       "      <td>5.145917</td>\n",
       "      <td>5.145917</td>\n",
       "      <td>5.145917</td>\n",
       "      <td>13.506125</td>\n",
       "      <td>68.725391</td>\n",
       "      <td>5.145917</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2012-01-04</td>\n",
       "      <td>5.176708</td>\n",
       "      <td>5.228729</td>\n",
       "      <td>5.176708</td>\n",
       "      <td>5.228729</td>\n",
       "      <td>17.221039</td>\n",
       "      <td>91.624089</td>\n",
       "      <td>5.195443</td>\n",
       "      <td>0.010049</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Timestamp      Open      High       Low     Close  Volume_(BTC)  \\\n",
       "0 2011-12-31  4.472552  4.472624  4.472552  4.472624      7.590527   \n",
       "1 2012-01-01  4.680778  4.680778  4.680778  4.680778      5.861697   \n",
       "2 2012-01-02  5.000000  5.000000  5.000000  5.000000     11.566478   \n",
       "3 2012-01-03  5.145917  5.145917  5.145917  5.145917     13.506125   \n",
       "4 2012-01-04  5.176708  5.228729  5.176708  5.228729     17.221039   \n",
       "\n",
       "   Volume_(Currency)  Weighted_Price  day_diff  \n",
       "0          34.069690        4.472579  0.000016  \n",
       "1          27.856539        4.680778  0.000000  \n",
       "2          57.832389        5.000000  0.000000  \n",
       "3          68.725391        5.145917  0.000000  \n",
       "4          91.624089        5.195443  0.010049  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add a value day_diff to df_bitstamp *day_diff = (close price - open price) / open price\n",
    "kwargs = { 'day_diff': lambda x: (x['Close']-x['Open'])/x['Open']}\n",
    "df_bitstamp = df_bitstamp.assign(**kwargs)\n",
    "df_bitstamp.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stock prices are commonly treated as random walks, which can be defined in these mathematical terms:\n",
    "$$\\begin{align}\n",
    "PredPrice_{t} &amp; = ActualPrice_{t-1} * \\epsilon, \\epsilon \\sim N(\\mu, \\sigma)\n",
    "\\end{align}$$\n",
    "We'll determine μ and σ from the training sets and apply the random walk model to the Bitcoin test sets.\n",
    "<br>Data that follows random walks should be normally distributed. Therefore, first, to make sure the daily change in price follows a normal distribution, We'll plot the histogram of values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We'll set a split date between train and test set to 2017-06-01\n",
    "split_date = '2017-06-01'\n",
    "\n",
    "fig, ax1 = plt.subplots(1,1)\n",
    "ax1.hist(df_bitstamp['day_diff'].values, bins=300)\n",
    "ax1.set_xlim([-0.002, 0.002])\n",
    "ax1.set_title('Bitcoin Daily Price Changes')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "linkText": "Export to plot.ly",
        "plotlyServerURL": "https://plot.ly",
        "showLink": false
       },
       "data": [
        {
         "marker": {
          "color": "rgba(235, 115, 150, 0.5)"
         },
         "mode": "lines",
         "name": "Actual",
         "type": "scatter",
         "x": [
          "2017-06-01T00:00:00",
          "2017-06-02T00:00:00",
          "2017-06-03T00:00:00",
          "2017-06-04T00:00:00",
          "2017-06-05T00:00:00",
          "2017-06-06T00:00:00",
          "2017-06-07T00:00:00",
          "2017-06-08T00:00:00",
          "2017-06-09T00:00:00",
          "2017-06-10T00:00:00",
          "2017-06-11T00:00:00",
          "2017-06-12T00:00:00",
          "2017-06-13T00:00:00",
          "2017-06-14T00:00:00",
          "2017-06-15T00:00:00",
          "2017-06-16T00:00:00",
          "2017-06-17T00:00:00",
          "2017-06-18T00:00:00",
          "2017-06-19T00:00:00",
          "2017-06-20T00:00:00",
          "2017-06-21T00:00:00",
          "2017-06-22T00:00:00",
          "2017-06-23T00:00:00",
          "2017-06-24T00:00:00",
          "2017-06-25T00:00:00",
          "2017-06-26T00:00:00",
          "2017-06-27T00:00:00",
          "2017-06-28T00:00:00",
          "2017-06-29T00:00:00",
          "2017-06-30T00:00:00",
          "2017-07-01T00:00:00",
          "2017-07-02T00:00:00",
          "2017-07-03T00:00:00",
          "2017-07-04T00:00:00",
          "2017-07-05T00:00:00",
          "2017-07-06T00:00:00",
          "2017-07-07T00:00:00",
          "2017-07-08T00:00:00",
          "2017-07-09T00:00:00",
          "2017-07-10T00:00:00",
          "2017-07-11T00:00:00",
          "2017-07-12T00:00:00",
          "2017-07-13T00:00:00",
          "2017-07-14T00:00:00",
          "2017-07-15T00:00:00",
          "2017-07-16T00:00:00",
          "2017-07-17T00:00:00",
          "2017-07-18T00:00:00",
          "2017-07-19T00:00:00",
          "2017-07-20T00:00:00",
          "2017-07-21T00:00:00",
          "2017-07-22T00:00:00",
          "2017-07-23T00:00:00",
          "2017-07-24T00:00:00",
          "2017-07-25T00:00:00",
          "2017-07-26T00:00:00",
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     "metadata": {},
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   ],
   "source": [
    "split_date = '2017-06-01'\n",
    "import datetime\n",
    "np.random.seed(202)\n",
    "bt_r_walk_mean, bt_r_walk_sd = (df_bitstamp[df_bitstamp['Timestamp']< split_date]['day_diff']).mean(), \\\n",
    "                         (df_bitstamp[df_bitstamp['Timestamp']< split_date]['day_diff']).std()\n",
    "bt_random_steps = np.random.normal(loc = bt_r_walk_mean, scale = bt_r_walk_sd, \n",
    "                size = (max(df_bitstamp['Timestamp']).to_pydatetime() - datetime.datetime.strptime(split_date, '%Y-%m-%d')).days + 1)\n",
    "\n",
    "trace_0 = go.Scatter(x = df_bitstamp[df_bitstamp['Timestamp']>= split_date]['Timestamp'],\n",
    "                   y = df_bitstamp[df_bitstamp['Timestamp']>= split_date]['Close'],\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Actual\",\n",
    "                   marker = dict(color = 'rgba(235, 115, 150, 0.5)')\n",
    "                       )\n",
    "\n",
    "trace_1 = go.Scatter(x = df_bitstamp[df_bitstamp['Timestamp']>= split_date]['Timestamp'],\n",
    "                   y = df_bitstamp[(df_bitstamp['Timestamp']+ datetime.timedelta(days=1))>= split_date]['Close'].values[1:] * (1+bt_random_steps),\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Predict\",\n",
    "                   marker = dict(color = 'rgba(115, 120, 235, 0.5)')\n",
    "                       )\n",
    "\n",
    "data_3 = [trace_0, trace_1]\n",
    "layout_3 = go.Layout(height=400, width=550,\n",
    "                title='Random walk prediction', \n",
    "                xaxis_title=\"timestamp\",\n",
    "                yaxis_title=\"Price /USD\", \n",
    "                     xaxis=dict(range=['2017-06-01', '2018-12-31']))\n",
    "\n",
    "fig = dict(data = data_3, layout = layout_3)\n",
    "iplot(fig);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prediction line tracks very closely the actual price, since at each new time point, the value follows the true price and the random step is added for prediction. Meaning that errors aren't carried over to subsequent predictions, no matter how large the error is. \n",
    "\n",
    "The Bitcoin random walk is particularly deceptive, as the scale of the y-axis is quite wide, making the prediction line appear quite smooth."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Price prediction with Long Short Term Memory (LSTM)\n",
    "For the Bitcoin's price prediction, we're going to utilize a Long Short Term Memory (LSTM) model which is known to suit time-series data.(Theory behind LSTMs: [1](http://colah.github.io/posts/2015-08-Understanding-LSTMs/), [2](http://blog.echen.me/2017/05/30/exploring-lstms/), [3](http://www.bioinf.jku.at/publications/older/2604.pdf))\n",
    "Our LSTM model will use previous data to predict the next day's closing price.\n",
    "<br>We'll create a new dataframe called model_data.\n",
    "<br>The close_off_high represents the gap between the closing price and price high for that day. When High price equals to Close price, the value is -1. When Close price equals to Low price, the value is 1. \n",
    "<br>The volatility columns are simply the difference between high and low price divided by the opening price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add close_off_high, bt_volatility\n",
    "kwargs = {'close_off_high': lambda x: 2*(x['High']- x['Close'])/(x['High']-x['Low'])-1,\n",
    "          'volatility': lambda x: (x['High']- x['Low'])/(x['Open'])}\n",
    "model_data = df_bitstamp.assign(**kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# re-order model_data by the timestamp\n",
    "model_data = model_data.sort_values(by='Timestamp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remove open price, Timestamp, Volume_(Currency), daily highs and lows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# drop columns\n",
    "model_data = model_data[['Timestamp','Close','Volume_(BTC)','close_off_high','volatility']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# drop all the nulls model_data the data frame \n",
    "# (LSTM model would not work if there is null in the data)\n",
    "model_data.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split data frame to training/test data　\n",
    "training_set, test_set = model_data[model_data['Timestamp']<split_date], model_data[model_data['Timestamp']>=split_date]\n",
    "training_set = training_set.drop('Timestamp', axis=1)\n",
    "test_set = test_set.drop('Timestamp', axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the dataset is arranged in order of earliest to latest. The timestamp column is not needed anymore. \n",
    "\n",
    "We must decide how many previous days it will have access to. We'll use 10 days, as it's a nice round number. We build little data frames consisting of 10 consecutive days of data (called windows), so the first window will consist of the 0-9th rows of the training set (Python is zero-indexed), the second will be the rows 1-10, etc. Picking a small window size means we can feed more windows into our model.\n",
    "\n",
    "Deep learning models don't like inputs that vary wildly. Typically, you want values between -1 and 1. We'll normalise the inputs to the first value in the window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalization of 'Close','Volume_(BTC)'\n",
    "window_len = 10\n",
    "norm_cols = [['Close','Volume_(BTC)']]\n",
    "LSTM_training_inputs = []\n",
    "for i in range(len(training_set)-window_len):\n",
    "    temp_set = training_set[i:(i+window_len)].copy()\n",
    "    for col in norm_cols:\n",
    "        # deviding all the values in the columns by the value of the first row\n",
    "        temp_set.loc[:, col] = temp_set[col]/temp_set[col].iloc[0] - 1\n",
    "    LSTM_training_inputs.append(temp_set)\n",
    "LSTM_training_outputs = (training_set['Close'][window_len:].values/training_set['Close'][:-window_len].values)-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "LSTM_test_inputs = []\n",
    "for i in range(len(test_set)-window_len):\n",
    "    temp_set = test_set[i:(i+window_len)].copy()\n",
    "    for col in norm_cols:\n",
    "        temp_set.loc[:, col] = temp_set[col]/temp_set[col].iloc[0] - 1 \n",
    "    LSTM_test_inputs.append(temp_set)\n",
    "LSTM_test_outputs = (test_set['Close'][window_len:].values/test_set['Close'][:-window_len].values)-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume_(BTC)</th>\n",
       "      <th>close_off_high</th>\n",
       "      <th>volatility</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.169052</td>\n",
       "      <td>1.268754</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.010049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.371659</td>\n",
       "      <td>-0.167266</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.002965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.464819</td>\n",
       "      <td>-0.512264</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.003141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.494732</td>\n",
       "      <td>-0.631366</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.004134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.566810</td>\n",
       "      <td>-0.510114</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.000403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.513384</td>\n",
       "      <td>-0.869066</td>\n",
       "      <td>-0.591148</td>\n",
       "      <td>0.002740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.429561</td>\n",
       "      <td>-0.804193</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.012580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.545032</td>\n",
       "      <td>-0.540842</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.465353</td>\n",
       "      <td>-0.263106</td>\n",
       "      <td>-0.985697</td>\n",
       "      <td>0.003568</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Close  Volume_(BTC)  close_off_high  volatility\n",
       "0   0.000000      0.000000       -1.000000    0.000016\n",
       "4   0.169052      1.268754       -1.000000    0.010049\n",
       "5   0.371659     -0.167266       -1.000000    0.002965\n",
       "6   0.464819     -0.512264       -1.000000    0.003141\n",
       "9   0.494732     -0.631366        1.000000    0.004134\n",
       "11  0.566810     -0.510114       -1.000000    0.000403\n",
       "13  0.513384     -0.869066       -0.591148    0.002740\n",
       "14  0.429561     -0.804193        1.000000    0.012580\n",
       "17  0.545032     -0.540842        1.000000    0.000030\n",
       "18  0.465353     -0.263106       -0.985697    0.003568"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LSTM_training_inputs[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This table represents an example of our LSTM model input. The next table contains the next 10 days's dataset, meaning that it's single timepoint prediction. \n",
    "<br>We're now ready to build the LSTM model. This is actually quite straightforward with Keras, you simply stack componenets on top of each other. \n",
    "\n",
    "For LSTMs with Keras, I refered to several articles [1](https://qiita.com/yukiB/items/5d5b202af86e3c587843), [2](https://qiita.com/yuyakato/items/ab38064ca215e8750865). (both written in Japanese)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Work with numpy arraysespecially as we now only have numerical data\n",
    "LSTM_training_inputs = [np.array(LSTM_training_input) for LSTM_training_input in LSTM_training_inputs]\n",
    "LSTM_training_inputs = np.array(LSTM_training_inputs)\n",
    "LSTM_test_inputs = [np.array(LSTM_test_inputs) for LSTM_test_inputs in LSTM_test_inputs]\n",
    "LSTM_test_inputs = np.array(LSTM_test_inputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# import the relevant Keras modules\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Activation, Dense\n",
    "from keras.layers import LSTM\n",
    "from keras.layers import Dropout\n",
    "\n",
    "def build_model(inputs, output_size, neurons, activ_func=\"linear\",\n",
    "                dropout=0.25, loss=\"mae\", optimizer=\"adam\"):\n",
    "    model = Sequential()\n",
    "\n",
    "    model.add(LSTM(neurons, input_shape=(inputs.shape[1], inputs.shape[2])))\n",
    "    model.add(Dropout(dropout))\n",
    "    model.add(Dense(units=output_size))\n",
    "    model.add(Activation(activ_func))\n",
    "\n",
    "    model.compile(loss=loss, optimizer=optimizer)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the build_model functions constructs an empty model called \"model\" (model = Sequential), to which an LSTM layer is added. That layer has been shaped to fit our inputs (n x m tables, where n and m represent the number of timepoints/rows and columns, respectively). The function also includes more generic neural network features, like [dropout](https://machinelearningmastery.com/dropout-regularization-deep-learning-models-keras/) and [activation functions](https://dashee87.github.io/deep%20learning/visualising-activation-functions-in-neural-networks/). Now, we just need to specify the number of neurons to place in the LSTM layer (I've opted for 20 to keep runtime reasonable), as well as the data on which the model will be trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /Users/Rory/anaconda3/lib/python3.6/site-packages/tensorflow/python/ops/resource_variable_ops.py:435: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Colocations handled automatically by placer.\n",
      "WARNING:tensorflow:From /Users/Rory/anaconda3/lib/python3.6/site-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.cast instead.\n",
      "Epoch 1/50\n",
      " - 12s - loss: 0.0610\n",
      "Epoch 2/50\n",
      " - 12s - loss: 0.0405\n",
      "Epoch 3/50\n",
      " - 13s - loss: 0.0364\n",
      "Epoch 4/50\n",
      " - 14s - loss: 0.0335\n",
      "Epoch 5/50\n",
      " - 12s - loss: 0.0316\n",
      "Epoch 6/50\n",
      " - 12s - loss: 0.0300\n",
      "Epoch 7/50\n",
      " - 13s - loss: 0.0307\n",
      "Epoch 8/50\n",
      " - 14s - loss: 0.0300\n",
      "Epoch 9/50\n",
      " - 32s - loss: 0.0296\n",
      "Epoch 10/50\n",
      " - 29s - loss: 0.0301\n",
      "Epoch 11/50\n",
      " - 14s - loss: 0.0286\n",
      "Epoch 12/50\n",
      " - 21s - loss: 0.0280\n",
      "Epoch 13/50\n",
      " - 21s - loss: 0.0283\n",
      "Epoch 14/50\n",
      " - 20s - loss: 0.0288\n",
      "Epoch 15/50\n",
      " - 20s - loss: 0.0285\n",
      "Epoch 16/50\n",
      " - 20s - loss: 0.0279\n",
      "Epoch 17/50\n",
      " - 19s - loss: 0.0279\n",
      "Epoch 18/50\n",
      " - 21s - loss: 0.0292\n",
      "Epoch 19/50\n",
      " - 21s - loss: 0.0280\n",
      "Epoch 20/50\n",
      " - 21s - loss: 0.0281\n",
      "Epoch 21/50\n",
      " - 21s - loss: 0.0275\n",
      "Epoch 22/50\n",
      " - 21s - loss: 0.0272\n",
      "Epoch 23/50\n",
      " - 22s - loss: 0.0279\n",
      "Epoch 24/50\n",
      " - 15s - loss: 0.0274\n",
      "Epoch 25/50\n",
      " - 14s - loss: 0.0287\n",
      "Epoch 26/50\n",
      " - 13s - loss: 0.0280\n",
      "Epoch 27/50\n",
      " - 15s - loss: 0.0282\n",
      "Epoch 28/50\n",
      " - 15s - loss: 0.0269\n",
      "Epoch 29/50\n",
      " - 13s - loss: 0.0265\n",
      "Epoch 30/50\n",
      " - 14s - loss: 0.0284\n",
      "Epoch 31/50\n",
      " - 13s - loss: 0.0275\n",
      "Epoch 32/50\n",
      " - 15s - loss: 0.0275\n",
      "Epoch 33/50\n",
      " - 13s - loss: 0.0272\n",
      "Epoch 34/50\n",
      " - 13s - loss: 0.0283\n",
      "Epoch 35/50\n",
      " - 14s - loss: 0.0274\n",
      "Epoch 36/50\n",
      " - 17s - loss: 0.0271\n",
      "Epoch 37/50\n",
      " - 20s - loss: 0.0276\n",
      "Epoch 38/50\n",
      " - 20s - loss: 0.0276\n",
      "Epoch 39/50\n",
      " - 20s - loss: 0.0271\n",
      "Epoch 40/50\n",
      " - 20s - loss: 0.0279\n",
      "Epoch 41/50\n",
      " - 20s - loss: 0.0276\n",
      "Epoch 42/50\n",
      " - 20s - loss: 0.0277\n",
      "Epoch 43/50\n",
      " - 21s - loss: 0.0275\n",
      "Epoch 44/50\n",
      " - 19s - loss: 0.0275\n",
      "Epoch 45/50\n",
      " - 19s - loss: 0.0276\n",
      "Epoch 46/50\n",
      " - 19s - loss: 0.0273\n",
      "Epoch 47/50\n",
      " - 19s - loss: 0.0266\n",
      "Epoch 48/50\n",
      " - 19s - loss: 0.0275\n",
      "Epoch 49/50\n",
      " - 19s - loss: 0.0271\n",
      "Epoch 50/50\n",
      " - 20s - loss: 0.0268\n"
     ]
    }
   ],
   "source": [
    "# random seed for reproducibility\n",
    "np.random.seed(202)\n",
    "bit_model = build_model(LSTM_training_inputs, output_size=1, neurons = 20)\n",
    "# model output is next price normalised to 10th previous closing price\n",
    "LSTM_training_outputs = (training_set['Close'][window_len:].values/training_set['Close'][:-window_len].values)-1\n",
    "# train model on data\n",
    "# note: bit_history contains information on the training error per epoch\n",
    "bit_history = bit_model.fit(LSTM_training_inputs, LSTM_training_outputs, \n",
    "                            epochs=50, batch_size=1, verbose=2, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If everything went to plan, then we'd expect the training error to have gradually decreased over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1,1)\n",
    "\n",
    "ax1.plot(bit_history.epoch, bit_history.history['loss'])\n",
    "ax1.set_title('Training Error')\n",
    "\n",
    "if bit_model.loss == 'mae':\n",
    "    ax1.set_ylabel('Mean Absolute Error (MAE)',fontsize=12)\n",
    "# just in case you decided to change the model loss calculation\n",
    "else:\n",
    "    ax1.set_ylabel('Model Loss',fontsize=12)\n",
    "ax1.set_xlabel('# Epochs',fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See how well this modeel performs on testset. That number below the code represents the model's mean absolute error (mae) on the training set after the 50th training iteration (or epoch)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "linkText": "Export to plot.ly",
        "plotlyServerURL": "https://plot.ly",
        "showLink": false
       },
       "data": [
        {
         "marker": {
          "color": "rgba(235, 115, 150, 0.5)"
         },
         "mode": "lines",
         "name": "Actual",
         "type": "scatter",
         "x": [
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          "2017-06-12T00:00:00",
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          "2017-06-15T00:00:00",
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          "2017-06-19T00:00:00",
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          "2017-06-26T00:00:00",
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     "metadata": {},
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   ],
   "source": [
    "trace_ac = go.Scatter(x = model_data[model_data['Timestamp']>= split_date]['Timestamp'][window_len:],\n",
    "                   y = test_set['Close'][window_len:],\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Actual\",\n",
    "                   marker = dict(color = 'rgba(235, 115, 150, 0.5)')\n",
    "                       )\n",
    "\n",
    "trace_pre = go.Scatter(x = model_data[model_data['Timestamp']>= split_date]['Timestamp'][window_len:],\n",
    "                   y = ((np.transpose(bit_model.predict(LSTM_test_inputs))+1) * test_set['Close'].values[:-window_len])[0],\n",
    "                   mode = \"lines\",\n",
    "                   name = \"Predicted\",\n",
    "                   marker = dict(color = 'rgba(115, 120, 235, 0.5)')\n",
    "                      )\n",
    "            \n",
    "data_3 = [trace_ac, trace_pre]\n",
    "\n",
    "layout_3 = go.Layout(height=400, width=550,\n",
    "                title='Test Set: Single Timepoint Prediction', \n",
    "                xaxis_title=\"timestamp\",\n",
    "                yaxis_title=\"Price /USD\", \n",
    "                     xaxis=dict(range=['2017-06-01', '2018-12-31']))\n",
    "\n",
    "fig = dict(data = data_3, layout = layout_3)\n",
    "\n",
    "\n",
    "iplot(fig);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Single point predictions can be deceptive, as we saw in the random walk prediction. Looking more closely, you'll notice that, again, the predicted values regularly mirror the previous values (e.g. October). \n",
    "<br>LSTM model has partially reproducted a autregressive (AR) model of some order p, where future values are simply the weighted sum of the previous p values. We can define an AR model in these mathematical terms:\n",
    "$$\\begin{align}\n",
    "PredPrice_{t} &amp; = \\phi_0 + \\phi_1*Price_{t-1} + \\ldots + \\phi_p*Price_{t-p} + \\epsilon_t, \\ \\epsilon_t \\sim N(0, \\sigma)\\\n",
    "\\end{align}$$\n",
    "The good news is that AR models are commonly employed in time series tasks (e.g. stock market prices), so the LSTM model appears to have landed on a sensible solution. The bad news is that it's a waste of the LSTM capabilities, we could have a built a much simpler AR model in much less time and probably achieved similar results.([More complex does not automatically equal more accurate](https://pdfs.semanticscholar.org/696c/2fa5697f58914921ff37d69ced44ddea143f.pdf)).\n",
    "\n",
    "We'll now build LSTM models to predict crypto prices for the next 5 days."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/50\n",
      " - 23s - loss: 0.0815\n",
      "Epoch 2/50\n",
      " - 22s - loss: 0.0614\n",
      "Epoch 3/50\n",
      " - 20s - loss: 0.0570\n",
      "Epoch 4/50\n",
      " - 21s - loss: 0.0543\n",
      "Epoch 5/50\n",
      " - 20s - loss: 0.0542\n",
      "Epoch 6/50\n",
      " - 20s - loss: 0.0532\n",
      "Epoch 7/50\n",
      " - 15s - loss: 0.0542\n",
      "Epoch 8/50\n",
      " - 15s - loss: 0.0527\n",
      "Epoch 9/50\n",
      " - 13s - loss: 0.0530\n",
      "Epoch 10/50\n",
      " - 15s - loss: 0.0523\n",
      "Epoch 11/50\n",
      " - 17s - loss: 0.0521\n",
      "Epoch 12/50\n",
      " - 17s - loss: 0.0519\n",
      "Epoch 13/50\n",
      " - 12s - loss: 0.0525\n",
      "Epoch 14/50\n",
      " - 10s - loss: 0.0526\n",
      "Epoch 15/50\n",
      " - 12s - loss: 0.0521\n",
      "Epoch 16/50\n",
      " - 12s - loss: 0.0514\n",
      "Epoch 17/50\n",
      " - 12s - loss: 0.0514\n",
      "Epoch 18/50\n",
      " - 12s - loss: 0.0515\n",
      "Epoch 19/50\n",
      " - 12s - loss: 0.0505\n",
      "Epoch 20/50\n",
      " - 12s - loss: 0.0520\n",
      "Epoch 21/50\n",
      " - 12s - loss: 0.0513\n",
      "Epoch 22/50\n",
      " - 12s - loss: 0.0516\n",
      "Epoch 23/50\n",
      " - 12s - loss: 0.0514\n",
      "Epoch 24/50\n",
      " - 12s - loss: 0.0519\n",
      "Epoch 25/50\n",
      " - 12s - loss: 0.0521\n",
      "Epoch 26/50\n",
      " - 12s - loss: 0.0509\n",
      "Epoch 27/50\n",
      " - 12s - loss: 0.0511\n",
      "Epoch 28/50\n",
      " - 12s - loss: 0.0505\n",
      "Epoch 29/50\n",
      " - 12s - loss: 0.0514\n",
      "Epoch 30/50\n",
      " - 12s - loss: 0.0505\n",
      "Epoch 31/50\n",
      " - 12s - loss: 0.0509\n",
      "Epoch 32/50\n",
      " - 12s - loss: 0.0506\n",
      "Epoch 33/50\n",
      " - 12s - loss: 0.0506\n",
      "Epoch 34/50\n",
      " - 12s - loss: 0.0500\n",
      "Epoch 35/50\n",
      " - 12s - loss: 0.0522\n",
      "Epoch 36/50\n",
      " - 12s - loss: 0.0497\n",
      "Epoch 37/50\n",
      " - 12s - loss: 0.0502\n",
      "Epoch 38/50\n",
      " - 12s - loss: 0.0505\n",
      "Epoch 39/50\n",
      " - 12s - loss: 0.0506\n",
      "Epoch 40/50\n",
      " - 12s - loss: 0.0509\n",
      "Epoch 41/50\n",
      " - 12s - loss: 0.0504\n",
      "Epoch 42/50\n",
      " - 12s - loss: 0.0507\n",
      "Epoch 43/50\n",
      " - 12s - loss: 0.0504\n",
      "Epoch 44/50\n",
      " - 12s - loss: 0.0516\n",
      "Epoch 45/50\n",
      " - 12s - loss: 0.0507\n",
      "Epoch 46/50\n",
      " - 12s - loss: 0.0503\n",
      "Epoch 47/50\n",
      " - 12s - loss: 0.0497\n",
      "Epoch 48/50\n",
      " - 12s - loss: 0.0505\n",
      "Epoch 49/50\n",
      " - 12s - loss: 0.0495\n",
      "Epoch 50/50\n",
      " - 12s - loss: 0.0504\n"
     ]
    }
   ],
   "source": [
    "# random seed for reproducibility\n",
    "np.random.seed(202)\n",
    "\n",
    "# we'll try to predict the closing price for the next 5 days\n",
    "# change this value if you want to make longer/shorter prediction\n",
    "pred_range = 5\n",
    "\n",
    "# initialise model architecture\n",
    "bit_model = build_model(LSTM_training_inputs, output_size=pred_range, neurons = 20)\n",
    "\n",
    "# model output is next 5 prices normalised to 10th previous closing price\n",
    "LSTM_training_outputs = []\n",
    "for i in range(window_len, len(training_set['Close'])-pred_range):\n",
    "    LSTM_training_outputs.append((training_set['Close'][i:i+pred_range].values/\n",
    "                                  training_set['Close'].values[i-window_len])-1)\n",
    "LSTM_training_outputs = np.array(LSTM_training_outputs)\n",
    "\n",
    "# train model on data (same as single point prediction)\n",
    "# note: bit_history contains information on the training error per epoch\n",
    "bit_history = bit_model.fit(LSTM_training_inputs[:-pred_range], LSTM_training_outputs, \n",
    "                            epochs=50, batch_size=1, verbose=2, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8EaLRaOjhhx9ufvjhh5uH56xNo6Fs2iAiRwAfA9gihDhERE1CCBej/EYhhCsRHQfwGyHEOSk9C8DPAcwFYCuE+JWU/p8wjFnIlrafJ6XPAvBzIcSP+qpPfHy84FtFM8buV5+9X4jKizV4JC0Orn6DNx6OiHKFEPGW7p+Xl1ceHR1dN2gVYgOSl5fnER0dHdhb3pDNbiAiGYCDAP4ihDgkJVdLXQWQnmuk9OsA/I129wNws590v17SGWNszIpfEY55/x47qAECG1uGJEiQZiu8A6BQCJFulHUEwJPS6ycBfGCU/gQZTAfQLHVLnATwfSJyJSJXAN8HcFLKayWi6VJZTxgdizHGxiQbuTXcAkZcNzcbRYZqTMJMAKsBfE1EX0pp/wFgK4BMIloLoBLAY1LehzBMfyyBoTvhxwAghGggov8GcEHa7pdCiAbp9Xp8MwXyBHhmA2OMMTYgQxIkSGMLTN0g4+FethcAfmLiWBkAMnpJzwEQNYBqMsYYY8wIr7jIGGOMsV5xkMAYY4yxXnGQwBhj95nWdi1+tP0ccisah7sqbJTjIIExxu4zhVWt+PpGM/b9s3K4q8JGOQ4SGGPsPlNedwcAcLqwGrpO/TDXhnW5cuWKnIjitFotACAxMTFs+/bt7ve63LS0NN/FixcHWbIvBwmMMXafKau/gwmu1WhUa7jLwQIqlWqynZ3dVAcHh1h3d/fo5OTkwObm5kH/vszOzi5OTU2tN6c+hw8fVg52+ebgIIExxu4znXcKkPno+1gVkYe/F1QPd3VGpX379hWr1eqLOTk5BXl5eYrNmzf7GOfr9Xp0dnYOV/WGDAcJjDF2HxH6Dizz2YMWrTPqrWbh5KVbGGm3Hx5NgoKCtHPnzm0uLCy0T0hIiEhNTVVNnTp1goODw9TCwkLb+vp66+XLl48fN27cFE9PzynPPfecr06nAwDodDqsW7fOz9XVNdrPz2/yoUOHnI2PnZCQEJGenu7R9X7btm0ewcHBkQqFIjYkJCTy3LlzDkuWLAmqqqqSp6SkhDk4OMS+9NJLXgCQlZWliI2NnaBUKmMiIiImHTt2rLul4fLly/Jp06ZFKBSK2BkzZoTV1dVZvCbSkN8FkjHG2L2jqXoHfoo6HKxJxbyoYJwozENuRSPiA92Gu2qmvZ/nj5utDve0DF+lGqujr/W/4beVlJTIsrKynBcuXNh4/vx55YEDB9yOHj1aHB0d3a7X62nhwoXBnp6eutLS0vzW1lar+fPnh73xxhuajRs31qWnp487deqU84ULFwqUSqV+0aJFIabKycjIcH311Vd99+/fXzJr1ix1QUGBrVwuF4cPHy5TqVSOO3bsKF+yZEkrAJSVlcmWLVsWtnPnzrLk5OTmI0eOOK1atSqkoKAg39fXV5eSkhIcHx9/Ozs7u+js2bOK5OTksHnz5jVZctm4JYExxu4TutYL0NVlYl9xDKyU8Zgf5Q17mTUOfnFjuKs26qxcuTJUqVTGJCYmTpg+fXrrli1bqgBgxYoV9fHx8e0ymQw1NTXW2dnZzrt27ap0cnLSq1Qq3YYNG6oPHDjgBgCHDh1yXb9+fU1oaKjWy8urc9OmTbdMlZeRkeGRmpp6a/bs2WorKytERUV1hIeHa3rbdvfu3e5z5sxpXrFiRbO1tTWSkpJaoqKi7hw8eNC5uLhYnp+fr0hPT79pb28vFixYcHvu3LkWBQgAtyQwxth9QeiaoKn8NdrIH69dnIOMGAUUtjZYEOWNY1/dxC9+NAl2MuvhrmbvLPiFf6/t2bOnpOuXuzF/f//uL+6SkhK5TqcjHx+f6K40IQR5e3trAKC6uloWEBDQvX1ISEiHqfKqqqrkoaGhJvONVVRUyE+cOOGqVCq7uy90Oh0lJia2VlZWypRKpc7Jyal7WktAQIDm+vXrcnOO3RMHCYwxdh/Q1h+F0DXifEcaOjpbEOihAAAsi/PDoYs3cLqwGj+c4jvMtRz9DDcaNggODtbK5XLR0NDwpUwm+862np6e2srKyu4v56tXr9qaOq6Pj4+mpKTEZL4xf39/TVJSUv2+ffsqeuYVFRXJW1tbbVpaWqy6AoVr167Jjet9N7i7gTHGRjkh9NA1fAgrx1h8VesOWxsr+DjZAQCmB7vDXmaNi5UWtzgzE8aPH6+dOXNm87p16/wbGhqsOjs7cenSJdvjx487AsDSpUsbd+7c6VlaWiqrra21fu2117xNHWvNmjV1O3bs8P7kk08c9Ho98vPzbYuKiuQA4OHhoTUOINauXVt/+vRpl4MHDzrpdDqo1Wo6duyYsrS0VBYeHq6JjIy888ILL/i2t7fTyZMnHc+cOeNi6TlykMAYY6Oc/vYXEJoqyNx+iLK6Oxjv7gArK8MvR2srgpeTLWpazWrJZncpMzOzXKPR0MSJE6NcXFxikpOTQ27cuCEDgLS0tNo5c+a0xMXFRcbExExatGiRyUUr1qxZ05iWlla1evXqYEdHx9ikpKTQ2tpaawDYuHHjrW3btvkolcqYl19+2Ss0NFSbmZlZsnXrVh93d/cYlUo15fXXX/fS6/UEAHv37r2am5urcHNzi3nllVd8li5d2u9aDKbQWJ4aEx8fL3Jycoa7GowxNiDt5S+j8/aXcJi0H7N++yliA1yx/fHY7vzlO8+DAPz1Xx8YlPKIKFcIEW/p/nl5eeXR0dF1g1IZNmB5eXke0dHRgb3lcUsCY4yNYp2tuehszobMfRFaNVa43tiGCd7fXpzPU8ktCcwyHCQwxtgoJTrV6Lj2GsjWHzKv1bhcZRiMP8nH6VvbeSrtUNPSPhxVZKMcBwmMMTZKaesOQmhrYOv/c5CVLS7fagEATPD5dkuCl5Mt7mg6cbtDNxzVZKPYkAQJRJRBRDVElG+U9lci+lJ6lBPRl1J6IBG1GeX9r9E+cUT0NRGVENHvSJrTQURuRHSKiIqlZ9ehOC/GGBtOsnEpsA16FdaKyQCAwqoWuDjI4C3NbOji6WQYGM+tCexuDVVLwrsA5hsnCCFWCCFihBAxAA4COGSUXdqVJ4R41ij9LQDrAIRJj65jvgggSwgRBiBLes8YY/c1spLBximh+31hVSsmeCvRc068p9IQNPC4BHa3hiRIEEJkA2joLU9qDVgOYG9fxyAiHwBOQojzwjAl408AlkjZiwG8J71+zyidMcbGhE69wJVbrZjYYzwCYOhuAIBqbklgd2kkjEmYBaBaCFFslBZERBeJ6GMimiWlqQBcN9rmupQGAF5CiCoAkJ49TRVGROuIKIeIcmprawfvLBhjbBhVNqjRpu3ERO/vBgnjpJaEWm5JYHdpJAQJj+PbrQhVAAKEELEA0gDsISInAL2tKXnXizwIIXYJIeKFEPHjxo2zqMKMMTbSXLllmNkQ0WP6IwA42dnATmbF3Q3srg1rkEBENgCWAvhrV5oQokMIUS+9zgVQCiAchpYDP6Pd/QDclF5XS90RXd0SNfe+9owxNnKU198BAASNU3wnj4jgqbTj7oZhduXKFTkRxWm1WgBAYmJi2Pbt293vdblpaWm+ixcvDrJk3+FuSZgH4LIQorsbgYjGEZG19DoYhgGKV6VuhFYimi6NY3gCwAfSbkcAPCm9ftIonTHG7kt7D5/E5eLy7vcV9XfgrpDDye67NxoCpAWVWrglwRwqlWqynZ3dVAcHh1h3d/fo5OTkwObm5kH/vszOzi5OTU3td8lklUo1+fDhw99tIhoCQzUFci+A8wAiiOg6Ea2VslLw3QGLiQC+IqI8AAcAPCuE6Br0uB7AbgAlMLQwnJDStwJ4hIiKATwivWeMsfvSldIKnDjzD5Rdu9GdVlZ3p/vOj73xcrJDTSu3JJhr3759xWq1+mJOTk5BXl6eYvPmzT7G+Xq9Hp2dncNVvSEzVLMbHhdC+AghZEIIPyHEO1L6U0KI/+2x7UEhRKQQIloIMVUIcdQoL0cIESWECBFCbJBmOUAIUS+EeFgIESY99zqTgjHG7geHjp+Bs5Mj5j44rTutvE6NQHfTQcI4bkmwSFBQkHbu3LnNhYWF9gkJCRGpqamqqVOnTnBwcJhaWFhoW19fb718+fLx48aNm+Lp6Tnlueee89XpDItW6XQ6rFu3zs/V1TXaz89v8qFDh5yNj52QkBCRnp7u0fV+27ZtHsHBwZEKhSI2JCQk8ty5cw5LliwJqqqqkqekpIQ5ODjEvvTSS14AkJWVpYiNjZ2gVCpjIiIiJh07dqy7peHy5cvyadOmRSgUitgZM2aE1dXV2Vh6/hbvyBhjbOgVFF1FYUk5Vi1bAFu5HADQpunErZZ2BHk4mNzPy8kOrR06qDU6OMhH1p/+t/9y2P9GVY3pyg8ClY+n+pl/WXLtbvcrKSmRZWVlOS9cuLDx/PnzygMHDrgdPXq0ODo6ul2v19PChQuDPT09daWlpfmtra1W8+fPD3vjjTc0GzdurEtPTx936tQp5wsXLhQolUr9okWLQkyVk5GR4frqq6/67t+/v2TWrFnqgoICW7lcLg4fPlymUqkcd+zYUb5kyZJWACgrK5MtW7YsbOfOnWXJycnNR44ccVq1alVIQUFBvq+vry4lJSU4Pj7+dnZ2dtHZs2cVycnJYfPmzbPoXuHDPSaBMcbYXTj8t4/h6qxEntoJF8oNjaZdgxbH99GSECwNaCy42XLvK3kfWLlyZahSqYxJTEycMH369NYtW7ZUAcCKFSvq4+Pj22UyGWpqaqyzs7Odd+3aVenk5KRXqVS6DRs2VB84cMANAA4dOuS6fv36mtDQUK2Xl1fnpk2bbpkqLyMjwyM1NfXW7Nmz1VZWVoiKiuoIDw/X9Lbt7t273efMmdO8YsWKZmtrayQlJbVERUXdOXjwoHNxcbE8Pz9fkZ6eftPe3l4sWLDg9ty5cy0KEABuSWCMsVHjSmkFLpeUY8Gjc7H54zLsuXAdx5+bhfI6aWZDH2MSpgW6AQA+L2tAvPR6pLDkF/69tmfPnpKuX+7G/P39u7+4S0pK5Dqdjnx8fKK70oQQ5O3trQGA6upqWUBAQPf2ISEhJvt7qqqq5KGhoWb1B1VUVMhPnDjhqlQqu7svdDodJSYmtlZWVsqUSqXOyclJ35UXEBCguX79utycY/fEQQJjjI0SR/+eDaWjAu1OKgBXoNZ0InXvRcwJN6z50tfARTeFHGGejvhnWQN+8tAQVfg+ZLzkdXBwsFYul4uGhoYvZbLvzirx9PTUVlZWdn85X7161dbUcX18fDQlJSUm8435+/trkpKS6vft21fRM6+oqEje2tpq09LSYtUVKFy7dk3ec6luc3F3A2OMjQLXblbjq8ISzJ8zHedKGzHe3QGvPxaN3IpGvPVxKTwcbeFo2/fvvoQgN+RWNKJTf9fr0LFejB8/Xjtz5szmdevW+Tc0NFh1dnbi0qVLtsePH3cEgKVLlzbu3LnTs7S0VFZbW2v92muveZs61po1a+p27Njh/cknnzjo9Xrk5+fbFhUVyQHAw8NDaxxArF27tv706dMuBw8edNLpdFCr1XTs2DFlaWmpLDw8XBMZGXnnhRde8G1vb6eTJ086njlzxsXSc+QggTHGRoGz/8iFjbU1HkiIxfmr9UgMG4cfRfviiQfGQ63p7HPQYpeEIDfc7tChsIrHJQyWzMzMco1GQxMnToxycXGJSU5ODrlx44YMANLS0mrnzJnTEhcXFxkTEzNp0aJFjaaOs2bNmsa0tLSq1atXBzs6OsYmJSWF1tbWWgPAxo0bb23bts1HqVTGvPzyy16hoaHazMzMkq1bt/q4u7vHqFSqKa+//rqXXq8nANi7d+/V3NxchZubW8wrr7zis3Tp0n7XYjCFpFmEY1J8fLzIyckZ7mowxlifNBotnvvP1zFlYihiHnwIK3d/jrefiMcjk7zQoevE2ndz8ECIO37yUGifx7nZ1IYZW8/g5R9OwpoHLVqADwBARLlCiHhL98/LyyuPjo6us7gCbFDl5eV5REdHB/aWx2MSGGNshLuQVwB1WzvmzIjHh6X1sLEiPBBiWM3X1sYaf376e2Ydx9fFHj7Odsi7bvFgdzbGcJDAGGMjVFV1HY78PRuff5EPH08PTAwLREbeV/BU9j/+wBRPpS0a1dpBrim7X3GQwBhjI5S6rR25X5QcXsMAACAASURBVBVizsw4/GDuTBARmtRauDhYNJsNAKC0k6G1nYMEZh4OEhhjbIQKCfTD7371Auxsv5kZ19ymgYtD7zdxMofSzga3+G6QzEw8u4ExxkYw4wABABrV2gEFCU52MrS0cUsCMw+3JDDG2CjSpNbC2X4g3Q02aG3Xmb9D7R1gbz7QrgP0AtDe/3c+ZN/glgTGGBslhBBobtPAdUDdDTK0aTuh7dSb3Eat0eHjolpACEOAUNYI2NsASjngaXpVR3b/4ZYExhgbJdSaTmg7xcC6G+wNf/Zb23VwU/TeIrHt70V451wZ8hZGwflyHbAiEpgd+M0Gz1pcPBtlzG5JICJHIvIjIsd7WSHGGGMGN5va8GTGP1F323Dfn0a14V5BLgPqbjAEGKZmONzu0CHzwjXYCMD+eBHg7wTMGm9xeewbV65ckRNRnFZruPaJiYlh27dvd7/X5aalpfkuXrzYotWz+gwSiCiKiLYT0VUAzQAqATQTUSkR/Z6IJltSKGOMsf79/dItfFxUizOXawAYxiMAgPMAZzcAMDku4UDONbR26KAj4PNHg4HV0YCVZTcHGq1UKtVkOzu7qQ4ODrHu7u7RycnJgc3NzYPePZ+dnV2cmpra75LJKpVq8uHDh5WDXb45TJ40Ee0FsAdAFYBVADwAyKXn1QBuAPgLEe3rrxAiyiCiGiLKN0r7LyK6QURfSo8fGOVtJqISIrpCRI8apc+X0kqI6EWj9CAi+pyIionor0RkeZjNGGMjRG6lYWXEnPIGAECzNCvBdQDrJDhJLQmmZji8d74CYZ6GBuMrNgT4OVlc1mi2b9++YrVafTEnJ6cgLy9PsXnzZh/jfL1ej87O+38QZ1+R0R4hxBQhxK+FEP8QQjQKIXTS8z+EEL8RQkwB8GczynkXwPxe0t8QQsRIjw8BgIgmAUgBECnt8wcisiYiawA7ACwAMAnA49K2APCqdKwwAI0A1ppRJ8YYG9G+qDDcDyin3PDc1ZIw0HUSAKCll5aElnYtyuruYOlUP9jLrHGrmddTCAoK0s6dO7e5sLDQPiEhISI1NVU1derUCQ4ODlMLCwtt6+vrrZcvXz5+3LhxUzw9Pac899xzvjqd4drqdDqsW7fOz9XVNdrPz2/yoUOHnI2PnZCQEJGenu7R9X7btm0ewcHBkQqFIjYkJCTy3LlzDkuWLAmqqqqSp6SkhDk4OMS+9NJLXgCQlZWliI2NnaBUKmMiIiImHTt2rLul4fLly/Jp06ZFKBSK2BkzZoTV1dVZPP7Q5I5CiKPmHEAIccyMbbKJKNDMOi0GsE8I0QGgjIhKACRIeSVCiKsAILVgLCaiQgBzAayUtnkPwH8BeMvM8hhjbMS51dyOG01tULnY42rdHdS2dhiNSbA8SHC2Nz0moarJEBSoXA33eKgaokWXOipf9de3l/V/G8sBsLILUtsGbLp2t/uVlJTIsrKynBcuXNh4/vx55YEDB9yOHj1aHB0d3a7X62nhwoXBnp6eutLS0vzW1lar+fPnh73xxhuajRs31qWnp487deqU84ULFwqUSqV+0aJFIabKycjIcH311Vd99+/fXzJr1ix1QUGBrVwuF4cPHy5TqVSOO3bsKF+yZEkrAJSVlcmWLVsWtnPnzrLk5OTmI0eOOK1atSqkoKAg39fXV5eSkhIcHx9/Ozs7u+js2bOK5OTksHnz5ll0w4677mMhIn8iSiOifyGigXZUbSCir6TuCFcpTQXA+IO8LqWZSncH0CSE0PVIZ4yxUeuLSkPrwVrpbo25FQ3d3Q1OAwgS+mpJuNnUBgBQudjB29kOVdL7sWjlypWhSqUyJjExccL06dNbt2zZUgUAK1asqI+Pj2+XyWSoqamxzs7Odt61a1elk5OTXqVS6TZs2FB94MABNwA4dOiQ6/r162tCQ0O1Xl5enZs2bbplqryMjAyP1NTUW7Nnz1ZbWVkhKiqqIzw8XNPbtrt373afM2dO84oVK5qtra2RlJTUEhUVdefgwYPOxcXF8vz8fEV6evpNe3t7sWDBgttz5861+I5e/TZBENFRADuEEH8jIicAnwP4CoA/gJkA/s3Cst8C8N8AhPS8DcAaAL0FHgK9BzSij+17RUTrAKwDgICAgLurMWOMDZHcikbY2lhhxTR/vPq3y7hQ3ggrAuxl1rCTWVt83K4bQ/XWknCz2RAU+LrYw9vZDp+V9jumblBY8gv/XtuzZ09J1y93Y/7+/t1f3CUlJXKdTkc+Pj7RXWlCCPL29tYAQHV1tSwgIKB7+5CQkA5T5VVVVclDQ0NN5hurqKiQnzhxwlWpVHZ3X+h0OkpMTGytrKyUKZVKnZOTU/dCGAEBAZrr169bNJDFnH6KaQA+ll4vAvCVEGK+FDAUwMIgQQhR3fWaiN4G0NVtcR2GAKSLH4Cb0uve0usAuBCRjdSaYLx9b+XuArALAOLj400GE4wxNpwuVjZiip8zFLY2iPZ3QU55A8K9lANaSAkAbKytoJBbo7VdhyN5N9HcpsXq6YYpjjeb2mBtRfBU2sHX2R7VrR3o1AtYj7HZDX0xbkAPDg7WyuVy0dDQ8KVM9t3PxdPTU1tZWdn95Xz16lXb72wk8fHx0ZSUlJjMN+bv769JSkqq37dvX0XPvKKiInlra6tNS0uLVVegcO3aNbmlDf99zW74IxH9EYAzgB3S61cAOBBRBoA3ASilroKMuy2YiIxHiiYB6Jr5cARAChHZElEQgDAA/wRwAUCYNJNBDsPgxiNCCAHgIwDJ0v5PAvjgbuvDGGMjyY2mNgR5GFY3nBrgiks3W3CrpR3OA5jZ0EUp3b8h41wZdmWXdqdXNbXD28kO1lYEb2c7dOoFalvN+nE7Jo0fP147c+bM5nXr1vk3NDRYdXZ24tKlS7bHjx93BIClS5c27ty507O0tFRWW1tr/dprr3mbOtaaNWvqduzY4f3JJ5846PV65Ofn2xYVFckBwMPDQ2scQKxdu7b+9OnTLgcPHnTS6XRQq9V07NgxZWlpqSw8PFwTGRl554UXXvBtb2+nkydPOp45c8bF0nM0GSQIIX4shPgxgGIAHwL4fzBMgfyJEGINgKdhGAuwRnpvkjSd8jyACCK6TkRrAbxGRF8T0VcAHgLwM6ncSwAyYWil+JtUXqfUSrABwEkAhQAypW0BYBOANGmQozuAdyy5GIwxNlI0t2m7BxlODXCBTi9wobxhQIMWu3Tdv6G8/g5uNrV3L9F8s7kNPs52AND9XNXchor6OwMu836VmZlZrtFoaOLEiVEuLi4xycnJITdu3JABQFpaWu2cOXNa4uLiImNiYiYtWrSo0dRx1qxZ05iWlla1evXqYEdHx9ikpKTQ2tpaawDYuHHjrW3btvkolcqYl19+2Ss0NFSbmZlZsnXrVh93d/cYlUo15fXXX/fS6/UEAHv37r2am5urcHNzi3nllVd8li5danG/ERl+iPexAdFCAHsBKADsEkKsl9KTATwmhFhhaeHDLT4+XuTk5Ax3NRhj7Fs6dJ2IeOlv2PhoBH7yUChqWtuRsCULALAgyhtvrYob0PGXvfUPtGk6UVDVAgDI3vgQAtwdkPjaR4jxd8HvHo9Fwc0W/OB3n2B+pDf+dukWjqU+iCiVoQuciHKFEPGWlp+Xl1ceHR1dN6CTYIMmLy/PIzo6OrC3vH5nNwghjgNwA+DWFSBIzgB4ZlBqyBhjrFvPWQyeSjv4udoDAFwGpbvBBkXV34zJq2xQQ68XuNXcDl8XQzldLQl/u2QYkH+1jlsTxiKzpkBKiyg190hrEEK03JtqMcbY2NXctfyyUddCbIBhlvhAFlLqorSTQaf/phW5skGNujsd0HTq4eti112Orc03XxFjeTrkWNbXwMVDRDStr52JaBoRHRr8ajHG2NjV1ZLwrSDB3zD2bDDGJDhJayVYWxFk1oTKBnX3Qkq+zoaWBCJCoLsCMf4uUNraoIpXXxyT+poC+b8wLInsBMMUyCsAWgEoAYQDmAOgCcBL97iOjDE2pvQaJAQYggRXE7d3vhtdd4L0d7UHEeFag7p7ISUfqSUBAHY/GQ+FrQ1W7DyPqmZuSRiL+lqW+e8A/k5E8TDcL+F7AFxguDfCVwBShBAXh6SWjDE2hvQWJMT4u2Dr0smYH2VyFp3ZulZdDPRQQC+Aa41q3JRaClTSmAQA8HczrJTs42LPLQljVL+LKQkhcgDwFADGGBsivQUJRISUhMFZJbZrQGSguwI6vR5fXW9Cwc0WONrafKvMLj5Odiis4iFoY5HFd4ZijDF2b3TPbrC7N3+iu44bPE6Bdm0nmtRafPDlDaQk+KO3lfl8XOxQd7sDGp0ecpu7vuUPG8X402aMsRGmSa2F0tYGNtb35k90V2tBkIcCAVKXggDwr4m936TQx9kOQgDVQ3RXSDZycJDAGGMjTEubdkB3euzPzFAP/GbpZMwI8eged7Ao2rf7dU8+0owHHpcwMFeuXJETUZxWa2gpSkxMDNu+fbv7vS43LS3Nd/HixUGW7MtBAmOMjTDGSzLfCzJrKzyeEABrK8IEbyekzg3FxkcjTG5vvETzWKBSqSbb2dlNdXBwiHV3d49OTk4ObG5uHvTvy+zs7OLU1NR+l0xWqVSTDx8+rBzs8s1h9kkT0SNE9I5062gQUTwRzb13VWOMsbHpXgcJxqytCM9/P6J7pcXe+LiMvZaEffv2FavV6os5OTkFeXl5is2bNxvflBB6vR6dnZ3DVb0hY1aQQESpAN6C4WZPiVJyG4Bf3aN6McbYmDWUQYI5HG1toLSzQWWDGq/+7fJwV2dIBQUFaefOndtcWFhon5CQEJGamqqaOnXqBAcHh6mFhYW29fX11suXLx8/bty4KZ6enlOee+45X51OBwDQ6XRYt26dn6ura7Sfn9/kQ4cOORsfOyEhISI9Pd2j6/22bds8goODIxUKRWxISEjkuXPnHJYsWRJUVVUlT0lJCXNwcIh96aWXvAAgKytLERsbO0GpVMZERERMOnbsWHdLw+XLl+XTpk2LUCgUsTNmzAirq6uzeASsuTv+O4CHhRDlRLSpqx4ATLdPMcYYs8hICxIAQ5fD3n9Wop97Alrks/cL/Ztu3u59QMQgcfF1VE9fPfHa3e5XUlIiy8rKcl64cGHj+fPnlQcOHHA7evRocXR0dLter6eFCxcGe3p66kpLS/NbW1ut5s+fH/bGG29oNm7cWJeenj7u1KlTzhcuXChQKpX6RYsW9T4yFEBGRobrq6++6rt///6SWbNmqQsKCmzlcrk4fPhwmUqlctyxY0f5kiVLWgGgrKxMtmzZsrCdO3eWJScnNx85csRp1apVIQUFBfm+vr66lJSU4Pj4+NvZ2dlFZ8+eVSQnJ4fNmzevyZLrZm53gxJA18Xt+iciA6CxpFDGGGOmNbVpB+UeDYPJ39UBNlaEbY9FD3dVhsTKlStDlUplTGJi4oTp06e3btmypQoAVqxYUR8fH98uk8lQU1NjnZ2d7bxr165KJycnvUql0m3YsKH6wIEDbgBw6NAh1/Xr19eEhoZqvby8Ojdt2nTLVHkZGRkeqampt2bPnq22srJCVFRUR3h4eK/fsbt373afM2dO84oVK5qtra2RlJTUEhUVdefgwYPOxcXF8vz8fEV6evpNe3t7sWDBgttz5861KEAAzG9JyAbwIoAtRmnPAfjI0oIZY4x9V7u2Exqd/p7ObvhWeZ06vHs5F36OzpjlEwhnuV2v2/3XokioNZ2I8B788XOW/MK/1/bs2VPS9cvdmL+/f/cXd0lJiVyn05GPj0935CSEIG9vbw0AVFdXywICArq3DwkJ6TBVXlVVlTw0NNRkvrGKigr5iRMnXJVKZXf3hU6no8TExNbKykqZUqnUOTk56bvyAgICNNevX7doPW9zg4RUAEeJ6BkASiK6AqAFwI8sKZQxxljveltt8V56u+CfOFphGGewq+CfWDMhHosCJ8Kqx6JKpqZHjjXGi00FBwdr5XK5aGho+FIm++7n5enpqa2srOz+cr569aqtqeP6+PhoSkpKTOYb8/f31yQlJdXv27evomdeUVGRvLW11aalpcWqK1C4du2avLdFssxh7q2iqwBMA7AcwEoATwL4nhDCZNMJY4yxuzeUQcJn1ZU4WnEZy4Ij8dasxYhy88IfLn2GLV98BJ1e3/8Bxrjx48drZ86c2bxu3Tr/hoYGq87OTly6dMn2+PHjjgCwdOnSxp07d3qWlpbKamtrrV977TWTN95Ys2ZN3Y4dO7w/+eQTB71ej/z8fNuioiI5AHh4eGiNA4i1a9fWnz592uXgwYNOOp0OarWajh07piwtLZWFh4drIiMj77zwwgu+7e3tdPLkScczZ864WHqO5s5uiAHgJ4T4pxBivxDiMwAqIhobnVOMMTZEhjJI+L+ySwh2csOPI+IR4uyOLQnfx9MTp+GTqnK8+uXH6ORAoV+ZmZnlGo2GJk6cGOXi4hKTnJwccuPGDRkApKWl1c6ZM6clLi4uMiYmZtKiRYsaTR1nzZo1jWlpaVWrV68OdnR0jE1KSgqtra21BoCNGzfe2rZtm49SqYx5+eWXvUJDQ7WZmZklW7du9XF3d49RqVRTXn/9dS+9Xk8AsHfv3qu5ubkKNze3mFdeecVn6dKl/a7FYAoJM4aqElE+gEVCiKtGaSEA/k8IMcWM/TMA/BBAjRAiSkr7LQzdFRoApQB+LIRoIqJAAIUw3JoaAD4TQjwr7RMH4F0A9gA+BPBTIYQgIjcAfwUQCKAcwHIhhMkPo0t8fLzIyeF7VzHGRo7TBdV4+k85+OAnMxHtb/EPQLNoOnVo0rTD097xW+mZpV/jryV5+N3MH0Hl6Pyd/YgoVwgRb2m5eXl55dHR0XWW7s8GV15enkd0dHRgb3nmzm4IMA4QAEAIUQrDl7I53gUwv0faKQBRUpBRBGCzUV6pECJGejxrlP4WgHUAwqRH1zFfBJAlhAgDkCW9Z4yxUadpCFsS5NY23wkQAGB5yGTsnrOs1wCBjS3mBgnXiWiqcYL0/qY5OwshsgE09Ej7uxBCJ739DIBfX8cgIh8ATkKI88LQ/PEnAEuk7MUA3pNev2eUzhhjo0rdbcMAdzeFDNDfg0UJzORqa3oFRjZ2mBskvAHgAyJKJaIfSCsw/h+A9EGqxxoAJ4zeBxHRRSL6mIhmSWkqANeNtrkupQGAlzS4smuQpaepgohoHRHlEFFObW3tIFWfMcYGR2nNbUTYy+H0xzzgeNFwV4eNcWZNgRRCvE1ETQDWAvCHYWGl54UQBwZaASL6fwB0AP4iJVXB0L1RL41BOExEkQB6m79x12G2EGIXgF2AYUyCZbVmjLF7Q1HWiP11WqC+Dpjo0f8OjN1DZq/nLITYD2D/YBZORE/CMKDxYakLAUKIDgAd0utcIioFEA5Dy4Fxl4QfvunuqCYiHyFEldQtUTOY9WSMsaEgLtzA/yu/g3pHGZx+9gDgMyw3/mOsm8kggYhWCyHel16vMbWdECLDkoKJaD6ATQBmCyHURunjADQIITqJKBiGAYpXhRANRNRKRNMBfA7gCQDbpd2OwLB2w1bp+QNL6sQYY8OmrBF490vkWgOlC4LxLxwgsBGgr5aExwG8L71ebWIbAaDfIIGI9gKYA8CDiK4D+AUMsxlsAZySVoLqmuqYCOCXRKQD0AngWSFE16DH9fhmCuQJfDOOYSuATCJaC6ASwGP91YkxxkYMTSfwXh40jnI8Aw3+4MezCtjIYDJIEEL8AADI8A2+FkCl0WyEuyKEeLyX5HdMbHsQwEETeTkAonpJrwfwsCV1Y4yxYaXtBN77Eqi5g+xHAtH6eTlCPb87LZGx4dDv7AZprMDXAHjpLcYYG0y3NcDvPgcu3gKWTcSn1oCjrQ28nXq/yRIb3a5cuSInojit1rAWRmJiYtj27dvd73W5aWlpvosXLw6yZF9zp0BehGHwIGOMscHSrgMa24G1scDDwSipuY2QcYpv3USIDT2VSjXZzs5uqoODQ6y7u3t0cnJyYHNzs7nfl2bLzs4uTk1N7XfJZJVKNfnw4cPDMkjF3JM+C+BvRPRfRLSWiNZ0Pe5h3Rhj7P7m4QD8YjYQ5wsAKK29jRDuahgR9u3bV6xWqy/m5OQU5OXlKTZv3uxjnK/X69HZ2Tlc1Rsy5gYJMwGUAZgNYBUMAxlXS68ZY4xZSmYNAMi71oSq5nZE+93b+zWwuxMUFKSdO3duc2FhoX1CQkJEamqqaurUqRMcHBymFhYW2tbX11svX758/Lhx46Z4enpOee6553x1OsPwPZ1Oh3Xr1vm5urpG+/n5TT506NC3RqQmJCREpKendy+GsW3bNo/g4OBIhUIRGxISEnnu3DmHJUuWBFVVVclTUlLCHBwcYl966SUvAMjKylLExsZOUCqVMREREZOOHTvW3dJw+fJl+bRp0yIUCkXsjBkzwurq6sxe7qAncxdTesjSAhhjjPVvx0clcLaXYVlcnyvU35e25X3iX97S6HAvywh0clU/Hz3r2t3uV1JSIsvKynJeuHBh4/nz55UHDhxwO3r0aHF0dHS7Xq+nhQsXBnt6eupKS0vzW1tbrebPnx/2xhtvaDZu3FiXnp4+7tSpU84XLlwoUCqV+kWLFoWYKicjI8P11Vdf9d2/f3/JrFmz1AUFBbZyuVwcPny4TKVSOe7YsaN8yZIlrQBQVlYmW7ZsWdjOnTvLkpOTm48cOeK0atWqkIKCgnxfX19dSkpKcHx8/O3s7Oyis2fPKpKTk8PmzZvXZMl167MlgYgciOjXRHRE6mqw7Wt7xhhjd+/KrVb8vaAaT84IhKOtxT/62CBauXJlqFKpjElMTJwwffr01i1btlQBwIoVK+rj4+PbZTIZampqrLOzs5137dpV6eTkpFepVLoNGzZUHzhwwA0ADh065Lp+/fqa0NBQrZeXV+emTZtumSovIyPDIzU19dbs2bPVVlZWiIqK6ggPD9f0tu3u3bvd58yZ07xixYpma2trJCUltURFRd05ePCgc3FxsTw/P1+Rnp5+097eXixYsOD23LlzLQoQgP5bEn4PYBoM6xEkA3AHkGppYYwxxr6h0enxn4fzcfjLG1DIrfHjGYHDXaVhYckv/Httz549JV2/3I35+/t3f3GXlJTIdTod+fj4RHelCSHI29tbAwDV1dWygICA7u1DQkI6TJVXVVUlDw0NNZlvrKKiQn7ixAlXpVLZ3X2h0+koMTGxtbKyUqZUKnVOTk7dMxIDAgI0169fl5tz7J76CxIWAJgqLXe8HUA2OEhgjLFBcfzrm/hrzjU8FueHp2cFw1Vh0d9xNoSMZ54EBwdr5XK5aGho+FIm++6tvT09PbWVlZXdH+rVq1dNtsb7+PhoSkpKzGqt9/f31yQlJdXv27evomdeUVGRvLW11aalpcWqK1C4du2a3NIZM/0NXFQY3V3xGgBeBowxxgbJn85XIHicAq8lT0GENy/DPNqMHz9eO3PmzOZ169b5NzQ0WHV2duLSpUu2x48fdwSApUuXNu7cudOztLRUVltba/3aa695mzrWmjVr6nbs2OH9ySefOOj1euTn59sWFRXJAcDDw0NrHECsXbu2/vTp0y4HDx500ul0UKvVdOzYMWVpaaksPDxcExkZeeeFF17wbW9vp5MnTzqeOXPG4tGw/QUJNkT0EBHNJaK5Pd9LaYwxxu5S/o1mXKxswurp43ldhFEsMzOzXKPR0MSJE6NcXFxikpOTQ27cuCEDgLS0tNo5c+a0xMXFRcbExExatGhRo6njrFmzpjEtLa1q9erVwY6OjrFJSUmhtbW11gCwcePGW9u2bfNRKpUxL7/8sldoaKg2MzOzZOvWrT7u7u4xKpVqyuuvv+6l1+sJAPbu3Xs1NzdX4ebmFvPKK6/4LF26tN+1GEwh6eaLvWcSlaPv2zELIUSwpYUPt/j4eJGTkzPc1WCMjUGbD32Nwxdv4LP/eBjO9t9tqh7JiChXCBFv6f55eXnl0dHRdYNZJ2a5vLw8j+jo6MDe8vockyCE6HUnxhhjA/P51Xo8GOYx6gIENrYM+jKTjDHG+tbarsXVujuYouJhXmxk4yCBMcaGWMHNFgBAFAcJbITjIIExxobY1zeaAXCQwEY+DhIYY+weE0KguU3b/T7/RjN8Paxxs6NhGGs1rDq7RuKz4SV9DnpT+XcVJBCRJxEFGz8GXEPGGLvP7c+5jgd+k4W62x3QC4F8dSWUEVV48+t/QN/HDLP72LmKigqXjo4OWV8z7Ni9pdfrqba21hlAvqltzFoknIjmA3gHgDcA4+hPALAeSCUZY+x+d7qwGmpNJ04VVqFAXwwrz3p4WLnitw88CqsxuEaCTqd7pqmpaX1ra+tTQgg3cKv2cNEDyNfpdE+b2sDcO4nsAPDfAN4TQrRZUhMiygDwQwA1QogoKc0NwF8BBAIoB7BcCNFIhpVF3gTwAwBqAE8JIb6Q9nkSwEvSYX8lhHhPSo8D8C4AewAfAvip4BCVMTbMOvUCn12th5WNHntunofGuh01Vx2x8eEH4G53T298OGLFxcVpYPgb/+Zw14X1zdzozRXATksDBMm7AOb3SHsRQJYQIgxAlvQeMNwzIkx6rAPwFtAdVPwCwPcAJAD4BRG5Svu8JW3btV/PshhjbMgV3GyBWnRg/OQmtFMb3JvHQzS6YEaox3BXjbF+mRskvAPgxwMpSAiRDaDnKJ3FAN6TXr8HYIlR+p+EwWcAXIjIB8CjAE4JIRqEEI0ATgGYL+U5CSHOS60HfzI6FmOMDYtWTQd+8/VpBE+rg61Ch5uFLvjH121YMzMICr4lNBsFzA0SpgN4i4iKiCjb+DHA8r2MbiBVBcBTSlcBML516HUpra/0672kfwcRrSOiHCLKqa2tHWD1GWPMNEeZHK1qPUSdG373wGK0NdnC0dYGT43RW0Kz0cfcUHa39BgqvY3kERakfzdRvn2ggAAAIABJREFUiF0AdgGGezdYWkHGGOtPS5sOJV8qsTzeD+HubnhqRhCCPBzg7MBLMbPRwawgoWtw4D1QTUQ+QogqqcugRkq/DsDfaDs/ADel9Dk90s9K6X69bM8YY8PmDx+XoF3XiZSEAADAyz+aNMw1YuzumAwSiGi1EOJ96fUaU9sJITIGUP4RAE8C2Co9f2CUvoGI9sEwSLFZCiROAvi10WDF7wPYLIRoIKJWIpoO4HMATwDYPoB6McbYgFQ1t+HdT8uxJEaFiT5Ow10dxizSV0vC4wDel16vNrGNAGBWkEBEe2FoBfAgouswzFLYCiCTiNYCqATwmLT5hzBMfyyBYQrkjwFACgb+G8AFabtfCiG6BkOuxzdTIE9ID8YYGxZ//LQceiGQ9kj4cFeFMYvRWF5KID4+XuTk5Ax3NRhj96EFb34CN4UMf3l6+nBXZdARUa4QIn6468HuPbNXuSIiVyJ6gog2S8+u/e/FGGNjT5Nag8u3WjA9yH24q8LYgJgVJBDRAwBKATwLYAqAfwVQKqUzxhgz8tnVBggBPBDCQQIb3cydAvk/AP5NCLGvK4GIVgD4HYBp96JijDE2Wn12tR72MmtM8XMZ7qowNiDmdjeEA8jskXYAQOjgVocxxka/z67WIz7QFXIbvm8RG93M/RdcDCClR9pjMHRBMMYYkzT8//buOz7KKm34+O+amkJ6JwQSSOhVmgKKIBZ0RXH1EV27rq6r7qu7++yrru/uPpbnsa1tV1ddC3bUR1Hsq+gCilRpoSWUAOm915k57x8zYMAEQkjIDLm+n898MnPuM/d93QPJXPc55z6nrplthTWcPFC7GlTg62h3w+3AxyLyG2AP3lUbM/Cu6qiUUsrnux2lAEzR8QjqBNDRGReXi8gg4DygL/AR8GmrOQqUUkoB32aXEh5k0/EI6oTQoSRBRJKBemPM663KokSkrzFGpz9WSinAGMOy7BKmpsditbS1pIxSgaWjYxI+4OC1EfC9Xti14SilVODaVVpHflUj0zJiezoUpbpER8ckDDbGbGpdYIzZJCJDuyEmpZQKKC0NLvIyS/m2oBKrgdMy4no6JKW6REeThBIRSTfG7NhfICLpQFn3hKWUUoEhd2MJqxdk0VDZhB24l2DWPPIDmWEOgiOcnH7LmJ4OUalO62h3w0vAeyLyMxEZLiLn450n4YXuC00ppfyb2+Xhh/d24AixEXnBAN4KbsY9KpKk4TGERAUhOi5BBbiOtiQ8CLQAjwIpeFdsfBF4rJviUkopv7W3rJ5lO0rYXVJH0uRoouND+duSHZAUxGU3jsVu1UmU1Imho0lCvDHmEeCR1oUikggUdnlUSinlh3aX1vE/n2RSXb6G8XG5jI8p5palF+Ix3qTgxasnaIKgTigdTRKygPA2yrcA0V0XjlJK+R9j3Liq17J57QL+MnwLEY5GDBYsQYNYO2UC5c1hCDAwrk9Ph6pUl+pokvCTjjURCQc8XRuOUkr5l+aiV3GVfohxlTEh2kGNfRLxqbOx9hmHWEMIAaJ6OkiluslhkwQR2QcYIFhE9h6yOQZ4q7sCU0qpnlRe18yzS3Zy89AirM7B3L8qmZ31I3j35tOx6IBE1UscqSXhCrytCJ8CV7YqN0CRMWb7sRxcRIYAb7cqGgj8CYgEfgmU+MrvNsZ86nvPXcD1gBv4jTHmC1/5OcCTgBV4wRjz4LHEppTq3V7+bjfPL93FovXjCHbYyKts4K1fjtEEQfUqh00SjDFLAEQk1hhT39UH9yUZY33HsAJ5eGdxvBZ43BjzaOv6IjIc72qUI/CuIfGViAz2bX4aOBPIBVaLyCJjzJaujlkpdeJzuT28vXofY/pFUFjdSGV9M2/9cjLjB+gQLNW7tJskiMgfjTEP+F7eKdJ29myM+VMXxXIGsNMYs6e9YwEXAAuMMU3AbhHZAUzybdthjNnli32Br64mCUr1Ynm1VQTb7EQHhRzV+xZvK6a4pokH5o5i8sBoXG5DdKijm6JUyn8driWh9VoNKe3UMV0YyzwOHuNwq4hcBawBfmeMqQCSgRWt6uT6ygD2HVI+uQtjU0oFgKr6Fh78YiuTRwTxffku1pXmMy99NNcNnXBU+3lr1V4Sw4OYMSQOm97SqHqxdpMEY8zNrZ5f251BiIgDmAPc5Sv6B3Af3iTkPuCvwHW0cZeFr05bv8VtJjAiciNwI0D//v2PKW6llP8wxnDbh9+Rw17WZrmIDQrh6iEn4ayL4KzHl/Dk3NEMC3GARcBphVDf80MU1zSyNKuEm08fpAmC6vU6egvkASISD0wDthhjtnVRHLOBH4wxRQD7f/qO90/gY9/LXA5u1egH7F+qur3ygxhjngeeB5gwYUJXtoQopXpAYV0NT69Zz6bKfOrD6gh128nLDufi8WO5OC2NmY8uYVxJA30fWX7wpYPNAol94IIhMCL+QPFHGwrwGJg7LvmnB1OqlzlsmiwiySLyvohsE5GXRWQEsBV4FtgoIvO6KI7LaNXVICJJrbbNBTJ9zxcB80TEKSJpQAawClgNZIhImq9VYp6vrlLqBPfsim2srMmmorGJxKZkFp47jwlRA3j48yxue3Md5xY18PcG2GcXHk5w4rliNFwyHE5PhQgnOA++VvpwfR4jk8NJjw/rmRNSyo8cqSXhWaAYuAO4FPgCuMEYs1BELsDbFbDgWAIQkRC8dyXc1Kr4YREZizfvz9m/zRizWUTewTsg0QXcYoxx+/Zzqy8+K/CSMWbzscSllPJ/NY0tfLC8nBEpg3ntqqkHbk98Yt5YbnnjB/61pYjZAyMw6QnkJIbwzNvrGRxs4cIpaW3ub2dJLRtzq7jnvGHH8zSU8ltHShKmAEnGmGYRWQJUAR8AGGM+FJFXjzUA362VMYeUXdlOdXx3XDzQRvmneOdzUEr1Ei9/l0NlnYs/nDHyoPkLwoPsvHTNRF5fsYeZQ+ORmFDO9RiGLd3F419lcd7opDbXWPhoQz4icP6YvsfzNJTyW0calWM3xjTDgS/zGmNM6149nVVEKdUjXG4PryzP4Yyh8YxJifzJdrvVwrVT0xgQEwqAxSLcMSuDPWX1fLWl6Cf1AT7PLGTCgCgSwoO6NXalAsWRWhJsIjKDH5OBQ19buy0ypZQ6jFU55ZTVNXPx+H5Hruwzc2g8cWFO3l+Xx+xRSQdt211ax7bCGv7fz4Z3dahKBawjJQnFwEutXpcd8rq4yyNSSqkO+GxTIcF2K6cPiT9yZR+b1cIFY/ryyvc5VNQ1E9VqgqTPM72r3p8zMrGrQ1UqYB22u8EYk2qMSTvc43gFqpRS+7k9hs83FzJjaBzBjqNr0Jx7UjItbsPHGw++S/rzzALG9IsgOTK4K0NVKqDpTCFKqYCzJqeckpomZo9MOnLlQwxPCmdIQhgL1+UdKFuaVcKG3CodsKjUITRJUEoFnOeW7iLMaWPG0I53NewnIswZ25cf9laSX9lAY4ub//dhJmmxoVxx8oBuiFapwKVJglKqe5mundh0WXYJX28r5taZ6fRxHvWksQCc6xu0+FlmIc/8eyd7yuq5/8KRBNl1LLZSrXXuN0wppY6k0QVLcmBtAfznFOiCL+Dyumbu/WgL/aKCuXpKaqf3kxYbyrCkcF5fsYe8igYuHNuXqemxxxyfUicaTRKUUl3LGFhXCO9shuomGBEH9S0QcWxJQlZRDdfNX01xTRPPXTn+mK/6fzY6iUe+2E54kI27Zg9l9YYtNDU1Ex7Wh7joSOJjo7BatWVB9W6aJCiluk6LG97YBKvyICUcbhwPA6MOqvKXRZspqm7kiXljcdp++iVsjAvTlIenuQgRC1gjcDsGceubP9DY4uHdm05pc/Kko3X+6L48uTibX02I5G/PzmdvXuFB24ODnAxNT+WS82fRL+noxz4odSLQJEEpdey2l8LeKlhfCLsr4dwMmJ0Oh0x9nJlXxfzlOQBY3tnAY/8xBqfNinHX4qpYjKtqCZ66zWCaDrzHEjKc+Xm/I6uolheumtAlCQJA/5gQ1v/pTBZ99jXZ9Q38+ppLSEtJorK6luLSCnbs3kvm9l04HfYuOZ5SgUhMFw8qCiQTJkwwa9as6ekwlAp8f1sJW0u9qypeNAwmtr3M8vXzV7M6p5xrpqbx1OJsgu1WLh8fxm8H3gemEXEOoNY6mvymFGxByQxJ6MP24mYunl/KaemxPPXzMTTVttBc58Ld4sbmtBIc4SQ0uvPTKDc1NYOA0+E4cmUFgIisNcZM6Ok4VPfTlgSl1LH7xWgIskFI+1fdn2wsYPG2Yv7z7CH8+vRBTEyN4sP1+by4IpcZSedzyqgzqDUDmfXIN1Q3uoBKBsa1UFHWwGwJYvrOFt7/w7c/2W/qxASmXDui06E7nZocKNUeTRKUUsdkV0ktn28uxCLCzKHxfLOtmNyKBmYOi2d6RhwWi/DO6n3c+f5GxvWP5NqpqYgIp2bEMS09lprGFq5bZOGdvol8sXkXNU0unr9yPPXNbp5dspMR8WFMzG6mT3oQQ6b3IzjcgSPEjs1hwdXsIShMuwOU6i7a3aDdDUp12uqcci597ns8h/wZCbJbaGzxcM2UVK46ZQBnP7GUkwfG8NyV4wlxHHxtUl7XzM+eWkZZXTMAs0cm8sS8cQfVaahqIjjC2a3nojpOuxt6D21JUEp12qL1+ThtVr763XRaXB6WZJUweWA0abGh3PfxFuYvz+H7nWU4bVb++h9jfpIgAESHOlh02zRuX7CetXsquOPMwT+powmCUj1DkwSlVKcYY/h6WzFT02MPLIqUGht6YPsfzx3OsuxSthfVcPu0JD5c9Dmr1m3G4/Fgt9sIcjqIjowgIS6aG6+Yy2vXT6KmyUV4kHYfKOUvNElQSnVKdnEteZUN3DIjvc3twQ4rT19+Eu+v3ceO7z+lsbGZk8ePJCw0hBaXi/qGJsorqygtr0READRBUMrP+EWSICI5QA3gBlzGmAkiEg28DaQCOcB/GGMqxPvX5EngXKAeuMYY84NvP1cD9/h2e78x5pXjeR5K9SZfbysG4PQhce3WGZkcwcjkCLYN70NyYhxhfULbrauU8j/+tMDTDGPM2FaDYe4EFhtjMoDFvtcAs4EM3+NG4B8AvqTiz8BkYBLwZxE5eKo3pVSX+XprMUMTw+jr62o4nKHpqZogKBWA/ClJONQFwP6WgFeAC1uVv2q8VgCRIpIEnA18aYwpN8ZUAF8C5xzvoJXqDbKLaliVU855vtUUlVInJn9JEgzwLxFZKyI3+soSjDEFAL6f+ydPTwb2tXpvrq+svfKDiMiNIrJGRNaUlJR08Wko1Tu8sGw3TpuFyyf37+lQlFLdyC/GJABTjTH5IhIPfCki2w5TV9ooM4cpP7jAmOeB58E7T0JnglWqscXN97vKODU9FpvVX3Lt7mWM4bPMQqobWli4Po+Lx/cjpo/emqjUicwvkgRjTL7vZ7GILMQ7pqBIRJKMMQW+7oRiX/VcIKXV2/sB+b7y0w8p/3c3h656ocr6Zm54ZQ1r9lRwysAYnrpsHHFhJ/6X5bNLdvHQ59783SJw/bS0Ho5IKdXdejxJEJFQwGKMqfE9Pwu4F1gEXA086Pv5oe8ti4BbRWQB3kGKVb5E4gvgv1sNVjwLuOs4noryU3XljexeWYDFamH4WQOOaV8rdpVx53sbya9o4OoJCXy6dgfzHt7NlZP6cd4pw4kO2oeraimehp2Y5nyMq8r7RksQwYMexxI8qAvO6PhbuC6Xhz7fxpwxfblt5iAaXC5CQjxkV5XS4HKRERFDsE1vX1TqRNPjSQKQACz03SdtA940xnwuIquBd0TkemAvcImv/qd4b3/cgfcWyGsBjDHlInIfsNpX715jTPnxOw3lbwq3lbPt633kby4DA/1Pij/ym9rR7PLw5zeWsmZ9JolSR6ppYvdSN8N827/+chsTY94jJHQ9WIJwOwaRWZZGZpEQFeJkxuAwgm0RB/bncXtoqGqmsaYZq82CI8RGcIQTsbTVa9azFq7L5U+LVzJyvIfiyG3ctmY9nkOmc//7tDkMjoztoQiVUt1F127QtRtOKMYYqvLr2PyvPexZXURQuINBU5IYNKUvfWKPfKteW6obW7jmpVUU7NzOEFPA8PT+DOiXSGxUBAnxMdidwdzx7iaSQ/fwyEUDiIg7jZvf3MLX24o5c3gCS7NLcHsMz88YRlBJE6W7qqjMr8Pj8hx0nEv+ehr24OObt3s8BkurxMQYQ1VBHYVby6nMr2N3TiX5RXWsnliLvV8zo6ITiAsOJchmJ9oZTJjdSbDNzuCIWELtuppib6FrN/Qe/tCSoFSXaKxp5tMHVtFY3YzFKgRPjCP19GTGpEV36P35lQ38c9kuxg+IIjrEwc7SOgbFhvLE4mw25VXx6BVnMmdsvwOzA7b21yv6MOfvbn77eTS/PLWezzcXcvusDG6fNZj8ygYu/sdyvv1oJ6luC3Fp4Qyenkx4QghB4Q48LkNzfQu2IGtXfyTtKqxq5O73VlNelc9NU2MZH5nG3vUu8jeXUVvSAECzQyhwu3CGOXhw4lRSh7c/aZJS6sSkLQnaknDCMMawZkEW0alhbKaF33yYic0i/GXOCK44ue2xCB5jaHK7aGoxzHtuBdsKa35SRwSemjeO88f0PezxX/0+hz8v2owAUSEOlvxhBn2c3jx8/b5Krn1mOen9Inj6yvHE9nGyOb+aFbvKOHd00oG1D7qLaSnHVbOKzB0r8DTuJsZRRlxw7YHtb35zOcE70qmPdvDv+jp2BYEryMrE1Cgev3QsQfbjl8Ao/6ctCb2HtiSoE8Ky7BI+3lCAOEAKmli4Lo/xA6IIC7JxzweZeIzhqlNScXs8fF+0l28L97CprJCyxno8vjtlo22hLM1IJzq/FlttMzabBXezG4sx2BdsgcpmmJ7abgxXnZJKakwo93yQyW0z0w8kCABjUyK577Kx/P7dDcx6bAkeA7VNLgDW7qng2SvHd8vn0tji5g//u5H0kA1cnzqfJHGQS1/yXSMJDs8gOqIf6/IMm8INn4U2IJ4mZo2L59MLRxEdqt0HSvV22pKgLQkB77NNBdz21jpCHFaCHVY8BpIjg/nnVROIDnVw02tr+HpbMVfPSGJdy1bqTRMRjiDGxiSxcXcdWQX1RITYuC0skZ9/WwUDIiA2xDvLht3ivd/PY2BsIozo/OBHgKyiGp78KpvoUAfj+keyKa+K+ctz+PKO6aTH9+maD8SnyeXmptfWsiSrhNRIwWaKuejkKfxqekabXSbGmDbLlTqUtiT0HpokaJIQ0DLzqrjg6e8YmxLJ/GsnEtbGKoJ1TS4uf2ElG/PLSRpSRVVhMCEt4cwZk8yL3+7mP88ewq9PH4S4jTcZcBy/pvWy2iamPvQ1c8b05eGLx7RZp8XtYW1WCY4VefQvrCOqohGrVaDFA00ucNogPRp+9ePf7PK6Zm5+fS0rd5fz4EWjuHRiCg0tbkIc2niojp0mCb2H/sVQAcsYw70fbSEqxM5L17SdIACEOm0svHkKlQ0tGGNYu6eCx77M4sVvdzM2JZKbThvovYK2Hf+r6Jg+Ti6dkMKbq/Zy2xnpVHhq2FZRDCIEWW2E2R0s+L6ApevL+aHcSq4FvrHB1PRY+saFehOEZjdEBh3Y57LsEu58bxMltU08celYLhznnZ1cEwSl1NHSvxoqYH2eWciqnHL+e+4oIoIPP5GPxSIH+tjPGpHI9CFxvLc2jxlD43p8WuUbTh3I6yv3cPN3C2mm+acVgiB1spWysRdS7XHz6qIt3F1QxnOzUpk5NOFANZfbw/2fbGX+8hwGxoby7k2nMCYl8jieiVLqRKPdDdrdEJAaW9yc+fgSQuw2PvnNtB7/oj9Wd7y9nm9Ld3D/eWOZ0jeF5TvL2F1Wy7q8UlbsK+K+ucOZM2gIAFX1LVzx4kqyi2v4xy/Gsyy7lJ0FZTQU76OmrJj+EXZmTRhGSt94oiLCiImKICoiDKtV71BQXUO7G3oPbUlQAWn+8hz2lTfw2vWTsJpa3PUF4KnH2mdcT4fWKTdNH8jCJ/LIzHJzcryF37+9iZpG790PV5+ScSBBAIgIsfPytRO5+B/LuXb+aiwCw6NtRBdvJyq0D3HBTj7+cimtLwBOHj+KX1998XE/L6VUYNMkQQWc/Ip6vlm3hBfO2sr4lleo3+xd+0tsMYSMeK+Ho+ucoYnhzBnTl2eX7GRnSS01jS6eumwcO4truXpK6k/qx/Zx8up1k3nh211cNqk/QxPDKK88mZgo79TPDQ2NlFVWU15ZTVl5JTHR2u2glDp62t2g3Q1+rb7ZxYvLdjOqXwTT0qPJ2fwglrpVJIRU45Fg7BEnYwkegsWZjNgTsYZk9HTInVZR18xZTyylpKaJn41O4u+Xn9TTISnVJu1u6D20JUH5rXV7K/jduxvYVVIHQKjDyjOnbqOFZByJ15Dc/xzEGtLDUXadqFAHj14yhns/2swdZw7u6XCUUkqTBOV/sotqePRf2/licxHxYU5euW4S+8rrWbe3ktr4hzljeMIJO03w9MFxLP7d6T0dhlJKAZokKD/z1OJsHv8qi1CHjTtmDeb6U9MOTG/c3voLSimluocmCcpvFFU38revs5k1LIGHfj5a1w5QSqkepklCZzS52LFyH+n1biirhwaXd3rcZje4fXP8zxrY01EGnPnLc3B7DPecN0wTBKWU8gOaJHTCppX7GLVgCwCeMAeWYDsE2bxz/jusYAvsiX16Qm2TizdW7GFmdC0L319EcWk5FosFi8WC2+3G4/Hg8RgeuPNmbDb9b6uUUseD/rXthGGT+vFBbhX/tTEPe5hw97kZXDC2b4dX0DPG0OTyEGS34vEYKuubiQoBxIqI//+TrNxVxhsr91JY1UhsmIOYUCcTUqOYM8b7GRhj2FhWSFljAzklDST3CWNScgKRwQ4+2VTAku0l1DW7OKl/FKcMiiEzr4q/f7OD6kYXKdGNFJXWkhAbDYDb7cZqtWK1WBCL0Ivv2FVKqeOuR+dJEJEU4FUgEfAAzxtjnhSRvwC/BEp8Ve82xnzqe89dwPWAG/iNMeYLX/k5wJOAFXjBGPPgkY5/rPMkbMqt4o8fbGJjbhXp8X24ZcYg5o7r1279xhY3zy3ZRUn+F8xIXMXQyDJCbI04rO4fK4kTZ+pfsIWf0um4utMbK/fwx4WZRATbGZIYRlltEyU1TVQ3urjqlAGcPTGM+dlr2VNTedD7jAFabIxcH87MOicZbrC6PAhgASw2CzFRwfT51QQkoWuXTFZKdS2dJ6H36OnLVhfwO2PMDyISBqwVkS992x43xjzaurKIDAfmASOAvsBXIrL/hvKngTOBXGC1iCwyxmzpzuBH9Yvgg19P5cMNefxz6W7ueHsDGfFhjEz2znq3bm8Fa3IqqGlswWm3snBdHjuKa7nzZA9pURa21YzAJeEEO51syGugrrGJscl2RoVG4coqoqqgDleLh+LaJioamgkJdZDWN4whk5OwhVgpaajD4zF8m13KO6tzCbbbiQsJYmR2BYOxMMRpJ8JuRdweWprdBDusSEQQ3NC5SXryKht48qOtXBQbyQ3j++OqbaGuopE6SyO59TU0/KuI1wr34hkMaa40vtlYzbzJycREWthcWkq+u5pro6MZ1dyMDAijxgLVjS7Cgu2E2a1IixtO0FsblVIqEPVokmCMKQAKfM9rRGQrkHyYt1wALDDGNAG7RWQHMMm3bYcxZheAiCzw1e3WJAG8qwvOHdePM4YlMO3Br3niq2ye+cVJPP5VFs8u2XlQ83hieBCvXT+JUzPOA6D10MaTXR6e/mYHt361g3mNuQxvzAfxNpdgDFaEOiCTIu4tW0V9SC0u4/lxB32hGigC7i5JxOky5ArkCrTgffRxWklxWIgGPB4P9Q2NuFze/n4Ap9OB0+nA1sZCQB6P4a73N5HSYmHCribW78pGBIIinIRGBzEoI5o9NY3syi4ha7cDqOf6aRncc9awg7th3B7wLcYU5nsopZTyTz3dknCAiKQC44CVwFTgVhG5CliDt7WhAm8CsaLV23L5ManYd0j55HaOcyNwI0D//v27LP7wIDs3nDqQx77M4uwnlrK7tI5LxyVww5QUYsOCsTmcBDvt7a5W6LBZuOPMwcwelcgDr69ncVEtxRaDxSbcc95wTh0cS2FZA0sziygsK6OpPIjmeitRIQ5mDU9gTEokLR43De4WYs8YQZNNqNhbydaCGowxOG0Wnvn3TsryCpl5z+O01NfS4nL9JI5hGWncdds1Pyl/7MsslmaVcP/sYZydFktwuIOgcAeWVudzKpCSVcJnmwq44uQBB1pUDhLgqzUqpVRv4hdrN4hIH2AJ8IAx5n0RSQBKAQPcByQZY64TkaeB740xr/ve9yLwKd5u7bONMTf4yq8EJhljbjvccbt67YbqxhamP/wNMe4qhpNPZUX5QduDnE6iI8M5/6xTmTpxTLv78XgMy3eW8fW2YmaPSmRiavRB25tdHvaW11NR38zYlEjsHfzirW1y8Yd3N5CzdhmN4qRJHHgQxGLh1IxYTs+IISoijJNPGgl4B1i+uzaXb7YV81lmIfMmpvA/F43q8ABNpdSJScck9B493pIgInbgPeANY8z7AMaYolbb/wl87HuZC6S0ens/IN/3vL3y4yY8yM5Xv51OYX4Bny1exqwpY4mKjKC5uZm6hkaqa2opr6wmJCjosPuxWIRpGbFMy4htc7vDZiE9/ugH9/Vx2nj6Fyex+KR+VNQ3ExZkZ0BMCC9/t5u31+TSb1Ast5304wJJH20s4A//u5HkyGAun9yfP58/XBMEpZTqRXo0SRDvN86LwFZjzGOtypN84xUA5gKZvueLgDdF5DG8AxczgFWAABkikgbk4R3cePnxOYuDxfRxEjM4lRGDU3vi8EckIswannBQ2UM/H01ji4cnFmczZVAU4xKqqS5fR0H2Wv7Id5mdAAAGN0lEQVRnmo2Lxg/EYi2B6lzcQWlYQ4b2UPRKKaWOp55uSZgKXAlsEpH1vrK7gctEZCze7oYc4CYAY8xmEXkH74BEF3CLMcYNICK3Al/gvQXyJWPM5uN5IoFMRLh/7kh+2FvBU58s4plpr2IHLh1kwWYRXMVLD9S1xczRJEEppXoJvxiT0FO6ekxCoNtdWsd1L3/HiLD1bK/qz29nn8bs0X0xxg2eeoyrFix2LPa2u0GUUr2DjknoPXq6JUH5kbTYUBbcdBrPfNOXv184gCGJ3hsURaxgDUOsesOiUkr1JpokqIMkhAfxXxeM7OkwlFJK+QG9aV0ppZRSbdIkQSmllFJt0iRBKaWUUm3SJEEppZRSbdIkQSmllFJt0iRBKaWUUm3SJEEppZRSbdIkQSmllFJt6tXTMotIDbC9p+PopFi8y2kHskA/B42/ZwVy/IEcO8AAY0xcTwehul9vn3Fxe6DOPy4iawI19v0C/Rw0/p4VyPEHcuyqd9HuBqWUUkq1SZMEpZRSSrWptycJz/d0AMcgkGPfL9DPQePvWYEcfyDHrnqRXj1wUSmllFLt6+0tCUoppZRqhyYJSimllGpTQCUJIpIiIt+IyFYR2Swi/8dXHi0iX4pItu9nlK98qIh8LyJNIvL7VvsZIiLrWz2qReT2do55johsF5EdInJnq3IRkQdEJMsXz28CKPZlrd6fLyIfBODnf4aI/OB7/7cikh5g8c/0xZ8pIq+IyBFvR+6h+F8SkWIRyTykvM1jBlD8l/hi8IjIEW9F9LPYHxGRbSKyUUQWikjkkeJXqtOMMQHzAJKAk3zPw4AsYDjwMHCnr/xO4CHf83hgIvAA8Pt29mkFCvFODtLWtp3AQMABbACG+7ZdC7wKWPYfK1BiP6Tee8BVAfj5ZwHDfM9/DcwPlPjxJuf7gMG+evcC1/tb/L7tpwEnAZmHlLd5zACKfxgwBPg3MCHAYj8LsPmeP9SRz14f+ujsI6BaEowxBcaYH3zPa4CtQDJwAfCKr9orwIW+OsXGmNVAy2F2ewaw0xizp41tk4AdxphdxphmYIHvWAA3A/caYzz7jxVAsQMgImHATKBDLQl+dg4GCPc9jwDyAyj+GKDJGJPlq/cl8HM/jB9jzFKgvI1NbR4zUOI3xmw1xnR4tlU/i/1fxhiX7+UKoF9Hz0OpoxVQSUJrIpIKjANWAgnGmALw/jLjzeI7ah7wVjvbkvFe8e2X6ysDGARcKiJrROQzEckIoNj3mwssNsZUH8UxAb84hxuAT0UkF7gSePAojtnT8ZcC9lbN3BcDKUdxzOMV/+EcyzH9If5O87PYrwM+O8Z9KNWugEwSRKQP3mby2zvzBddqPw5gDvBue1XaKNt/z6gTaDTeqVX/CbzUwWP6Q+z7XUYn/kj5yTncAZxrjOkHvAw8dhTH7dH4jTEG7xfE4yKyCqgBXG3Ube+4xyv+bhHI8ftT7CLyR7z/b97o7D6UOpKASxJExI73l/QNY8z7vuIiEUnybU8CDtv038ps4AdjTJHvvSmtBhT9Cu+VX+srvH782Kyd64sDYCEwOoBiR0Ri8DaHf9LB4/nNOYhIHDDGGLPSV/42MCVQ4gcwxnxvjDnVGDMJWApk+2H8h9OpY/pR/EfNn2IXkauBnwG/8CWdSnWLgFrgSUQEeBHYaoxpfeW4CLgab5Pz1cCHHdzlQVfSxph9wNhWx7MBGSKSBuThvfq73Lf5A7z9+S8B0/EOZAqU2AEuAT42xjR28Hj+dA4VQISIDPb165+Jt484UOJHROKNMcUi4gT+L94Bbn4V/xEc9TH9LP6j4k+xi8g5eP/PTDfG1HfweEp1jvGD0ZMdfQDT8DY3bwTW+x7n4h0Ithjv1dhiINpXPxHv1Vw1UOl7Hu7bFgKUARFHOOa5eBOAncAfW5VH4r0K3wR8j/fKNiBi9237N3BOAH/+c32f/QbfuQwMsPgfwZvYbMfbdO2vn/9bQAHeAXi5+O7CaO+YART/XN/rJqAI+CKAYt+Bd6zL/jiePZrfY33o42geOi2zUkoppdoUcGMSlFJKKXV8aJKglFJKqTZpkqCUUkqpNmmSoJRSSqk2aZKglFJKqTZpkqCUUkqpNmmSoJRSSqk2/X+cBHjE30jjCgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# little bit of reformatting the predictions to closing prices\n",
    "bt_pred_prices = ((bit_model.predict(LSTM_test_inputs)[:-pred_range][::pred_range]+1)*\\\n",
    "                   test_set['Close'].values[:-(window_len + pred_range)][::5].reshape(int(np.ceil((len(LSTM_test_inputs)-pred_range)/float(pred_range))),1))\n",
    "\n",
    "pred_colors = [\"#FF69B4\", \"#5D6D7E\", \"#F4D03F\",\"#A569BD\",\"#45B39D\"]\n",
    "fig, ax1 = plt.subplots(1,1)\n",
    "ax1.plot(model_data[model_data['Timestamp']>= split_date]['Timestamp'][window_len:],\n",
    "         test_set['Close'][window_len:], label='Actual')\n",
    "\n",
    "for i, (bt_pred) in enumerate(bt_pred_prices):\n",
    "    # Only adding lines to the legend once\n",
    "    if i<5:\n",
    "        ax1.plot(model_data[model_data['Timestamp']>= split_date]['Timestamp'][window_len:][i*pred_range:i*pred_range+pred_range],\n",
    "                 bt_pred, color=pred_colors[i%5], label=\"Predicted\")\n",
    "    else: \n",
    "        ax1.plot(model_data[model_data['Timestamp']>= split_date]['Timestamp'][window_len:][i*pred_range:i*pred_range+pred_range],\n",
    "                 bt_pred, color=pred_colors[i%5])\n",
    "\n",
    "ax1.set_title('Test Set: 5 Timepoint Predictions',fontsize=13)\n",
    "ax1.set_ylabel('Bitcoin Price ($)',fontsize=12)\n",
    "ax1.set_xlim('2017-06-01', '2017-12-31')\n",
    "ax1.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0., prop={'size': 12})\n",
    "\n",
    "plt.show()"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "The predictions are visibly less impressive than their single point counterparts. Nevertheless, the model returned somewhat nuanced behaviours. It didn't simply forecast prices to move uniformly in one direction. So there are some grounds for optimism.\n",
    "\n",
    "Moving back to the single point predictions, our deep machine artificial neural model looks okay, but so did that boring random walk model. Like the random walk model, LSTM models can be sensitive to the choice of random seed (the model weights are initially randomly assigned)."
   ]
  }
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