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Computational Mechanics 02 - Analyze Data

Learning some statistics and data processing skills in Python

Welcome to Computational Mechanics Module #2 - Analyze Data

There are four modules and one final project. The modules will get us started on our exploration of computational mechanics using Python, listed below each module are the learning objectives.

01_Cheers_Stats_Beers

  • Read data from a csv file using pandas.
  • The concepts of Data Frame and Series in pandas.
  • Clean null (NaN) values from a Series using pandas.
  • Convert a pandas Series into a numpy array.
  • Compute maximum and minimum, and range.
  • Revise concept of mean value.
  • Compute the variance and standard deviation.
  • Use the mean and standard deviation to understand how the data is distributed
  • Plot frequency distribution diagrams (histograms).
  • Normal distribution and 3-sigma rule.

02_Seeing_Stats

  • You should always plot your data.
  • The concepts of quantitative and categorical data.
  • Plotting histograms directly on columns of dataframes, using pandas.
  • Computing variance and standard deviation using NumPy built-in functions.
  • The concept of median, and how to compute it with NumPy.
  • Making box plots using pyplot.
  • Five statistics of a box plot: the quartiles Q1, Q2 (median) and Q3 (and
  • interquartile range Q3$-$Q1), upper and lower extremes.
  • Visualizing categorical data with bar plots.
  • Visualizing multiple data with scatter plots and bubble charts.
  • pandas is awesome!

03_Linear_Regression_with_Real_Data

  • Making our plots more beautiful
  • Defining and calling custom Python functions
  • Applying linear regression to data
  • NumPy built-ins for linear regression
  • The Earth is warming up!!!

04_Stats_and_Montecarlo

  • How to generate "random" numbers in Python$^+$
  • The definition of a Monte Carlo model
  • How to calculate $\pi$ with Monte Carlo
  • How to model Brownian motion with Monte Carlo
  • How to propagate uncertainty in a model with Monte Carlo

$^+$ Remember, the computer only generates pseudo-random numbers. For further information and truly random numbers check www.random.org

HW_02

Project #02 - NYSE random walk predictor

In the Stats and Monte Carlo module, you created a Brownian motion model to predict the motion of particles in a fluid. The Monte Carlo model took steps in the x- and y-directions with random magnitudes.

This random walk can be used to predict stock prices. Let's take a look at some data from the New York Stock Exchange NYSE from 2010 through 2017.

Important Note: I am not a financial advisor and these models are purely for academic exercises. If you decide to use anything in these notebooks to make financial decisions, it is at your own risk. I am not an economist/financial advisor/etc., I am just a Professor who likes to learn and exeriment.

Here, I will show an example workflow to analyze and predict the Google stock price [GOOGL] from 2010 - 2014. Then, you can choose your own stock price to evaluate and create a predictive model.

  1. Explore data and select data of interest
  2. Find statistical description of data: mean and standard deviation
  3. Create random variables
  4. Generate random walk for [GOOGL] stock opening price