chapter_1_lesson_1.qmd

---
title: "Course Introduction"
subtitle: "Chapter 1: Lesson 1"
format: html
editor: source
sidebar: false
---

```{r}
#| include: false
source("common_functions.R")
```

## Learning Outcomes

{{< include outcomes/_chapter_1_lesson_1_outcomes.qmd >}}



## Introduction to the course structure and Canvas (30 min)

-   Introduction of teacher(s)
-   Introduction of students
-   Syllabus
-   Software: R and RStudio
-   Textbook
    -   Cowpertwait, P. S. P., & Metcalfe, A. V. (2009). *Introductory Time Series with R*. Springer. ISBN 978-0-387-88697-8; e-ISBN 978-0-387-88698-5; DOI 10.1007/978-0-387-88698-5.
-   [Supplement to the Textbook](https://byuistats.github.io/timeseries_supplement)
    -   Modern R code
    -   Time Series (TS) Notebook for in-class activities
-   Lesson cadence
    -   Read assigned section(s) from the textbook
        -   Assigned sections listed in the TS notebook
    -   Reading Journals
        -   Record your learning
        -   Include all of the following from the assigned reading: vocabulary terms, nomenclature, models, important concepts, and your questions
        -   Review another student's learning journal at the beginning of class
    -   In-class Activities
    -   Homework
-   Assessment Structure
    -   Daily Homework, Multi-week Projects, Three Exams
-   Grading Categories
    -   Reading Journal (10%)
    -   Homework (40%)
    -   Projects (25%)
    -   Exams (25%)
-   Grades: 93% = A
-   Calendar
-   Team structure for class activities
    -   Random assignment, frequent changes, partner with each student in the class
    -   We are all in this together

## Class Activity: Google Trends (Searches for "Chocolate") (10 min)

Google Trends allows you to download a time series showing the proportional number of searches for a given term. The month with the highest number of searches has a value of 100. The values for the other months are given as a percentage of the peak month's value. The following table illustrates the data, as given by Google Trends.

```{r}
#| echo: false

if (!require("pacman")) install.packages("pacman")
pacman::p_load("tidyverse", "rio","mosaic")
chocolate_raw <- rio::import("https://byuistats.github.io/timeseries/data/chocolate_raw.csv") 

# Prints a few rows of the chocolate_raw data file.

temp <- chocolate_raw
temp[1,1] <- "Category:"
temp[1,2] <- paste0("All categories", strrep(" ",12))

temp2 <- temp |> 
  head(16) |> 
  bind_rows(data.frame(V1 = "⋮   ", V2 = "⋮")) |> 
  bind_rows(temp |> tail(3)) |> 
  mutate(
    V1 = 
      case_when(
        row_number() == 3 ~ paste0(V1, strrep(" ",4)),
        row_number() > 3 ~ paste0(V1, strrep(" ",2)),
        TRUE ~ V1
      )
  )

temp2 |> 
  rename(" " = "V1", "   " = "V2") |> print(row.names = FALSE)

```

The cleaned version of the data used for this demonstration are available in the file <a href="data/chocolate.csv" download>chocolate.csv</a>. We can read this directly into a data frame using the command 

`chocolate_month <- rio::import("https://byuistats.github.io/timeseries/data/chocolate.csv")`

In Lesson 3, we will practice converting data like this into a time series (tsibble) object.

```{r}
#| code-fold: true
#| code-summary: "Show the code"

if (!require("pacman")) install.packages("pacman")
pacman::p_load("tsibble", "fable",
               "feasts", "tsibbledata",
               "fable.prophet", "tidyverse",
               "patchwork", "rio")

# read in the data from a csv and make the tsibble
# change the line below to include your file path
chocolate_month <- rio::import("https://byuistats.github.io/timeseries/data/chocolate.csv")
start_date <- lubridate::ymd("2004-01-01")
date_seq <- seq(start_date,
                start_date + months(nrow(chocolate_month)-1),
                by = "1 months")
chocolate_tibble <- tibble(
  dates = date_seq,
  year = lubridate::year(date_seq),
  month = lubridate::month(date_seq),
  value = dplyr::pull(chocolate_month, chocolate)
)
chocolate_month_ts <- chocolate_tibble |>
  mutate(index = tsibble::yearmonth(dates)) |>
  as_tsibble(index = index)

chocolate_month_ts |> head()
```

For now, we will use the tsibble object (which in this case is called *chocolate_month_ts*) to explore the time series. Here is a plot of the time series representing the proportional frequency of searches for the term "chocolate."

```{r}
#| code-fold: true
#| code-summary: "Show the code"

autoplot(chocolate_month_ts, .vars = value) +
  labs(
    x = "Month",
    y = "Searches",
    title = "Relative Number of Google Searches for 'Chocolate'"
  ) +
  theme(plot.title = element_text(hjust = 0.5))
```

::: {.callout-tip icon=false title="Check Your Understanding"}

-   What do you notice about this plot?

:::

::: panel-tabset
#### Characteristics

#### Trend

The red line represents the mean for each year. The point for this line was positioned to align with July of the year.

```{r}
#| echo: false

chocolate_annual_ts <- summarise(index_by(chocolate_month_ts, year), value = mean(value))

temp <- chocolate_month_ts |> 
  filter(month == 7) |> 
  dplyr::select(-value) |> 
  right_join(chocolate_annual_ts, by = join_by(year))

autoplot(chocolate_month_ts, .vars = value) +
  labs(
    x = "Month",
    y = "Searches",
    title = "Relative Number of Google Searches for 'Chocolate'"
  ) +
  theme(plot.title = element_text(hjust = 0.5)) +
  geom_line(data = temp, 
            aes(x = index, y = value),
            color = "#D55E00")
```

:::: {.callout-tip icon=false title="Check Your Understanding"}

-   What do you observe about the number of searches for "chocolate" each month?
-   What might be causing this trend?

::::

#### Seasonality / Cycles

Consider the data for the last few years:

```{r}
#| echo: false

                            ####################### FUTURE MAINTENANCE ###################
first_year_selected <- 2020 # Increase this in future semesters, so the figure shows each year clearly. There should be a major vertical line for January of each year, and the shape of the monthly pattern should be clearly evident.

lastfew_plot <- autoplot(chocolate_month_ts |> filter(dates >= lubridate::mdy(paste0("07/01/", first_year_selected))), .vars = value) +
  labs(
    x = "Month",
    y = "Searches",
    title = "Relative Number of Google Searches for Chocolate (Select Months)"
  ) +
  theme(plot.title = element_text(hjust = 0.5))
lastfew_plot
```

:::: {.callout-tip icon=false title="Check Your Understanding"}

-   Which month tends to have the greatest number of Google searches for "chocolate"?
-   Which month has the second greatest number of Google searches for "chocolate"?
-   When do the fewest number of Google searches for "chocolate" occur?
-   How can you explain these observations?

::::

#### Autocorrelation

**Autocorrelation** is a fancy word that means that sequential values in a sequence of data are related in some way.

Consider searches in successive months. Are they independent?

```{r test}
#| echo: false

                        ####################### FUTURE MAINTENANCE ###################
example_year <- 2023   # Change this in future semesters to be the last full year with data.

lastfew_plot
```

:::: {.callout-tip icon=false title="Check Your Understanding"}

-   Think about what you know about the reported number of searches in December compared to the following February. The reported number of searches for "chocolate" in December `r example_year-1` is `r chocolate_month_ts |> filter(year == example_year - 1, month == 12) |> data.frame() |> dplyr::select(value) |> pull()`. Does it make sense that the reported number of searches in February `r example_year` is `r chocolate_month_ts |> filter(year == example_year, month == 2) |> data.frame() |> dplyr::select(value) |> pull()` ? Given the value from December, is the value in the following February independent and completely random?
-   The value reported by Google for June `r example_year` is `r chocolate_month_ts |> filter(year == example_year, month == 6) |> data.frame() |> dplyr::select(value) |> pull()`. Based on what you have observed in the data, do you think the value for July `r example_year` will be close to or far from this value? Justify your answer.

::::

:::

Discuss these vocabulary terms in the context of the Google Trends ("Chocolate") example: - Time series - Sampling interval - Autocorrelation (or serial dependence) - Trend - Seasonal variation - Cycle

```{r}
#| include: false

# TS Plot (Monthly and Annual)

mp <- autoplot(chocolate_month_ts, .vars = value) +
  labs(
    x = "Month",
    y = "Searches",
    title = "Relative Number of Google Searches for 'Chocolate'"
  ) +
  theme(plot.title = element_text(hjust = 0.5))
yp <- autoplot(chocolate_annual_ts, .vars = value) +
  labs(
    x = "Year",
    y = "Searches",
    title = "Mean Annual Google Searches for 'Chocolate'"
  ) +
  scale_x_continuous(breaks = seq(2004, max(chocolate_month_ts$year), by = 2)) +
  theme(plot.title = element_text(hjust = 0.5))

mp

# mp / yp
```

## Class Activity: S&P 500 (10 min)

The time series plot below illustrates the daily closing prices of the standard and Poor's 500 stock index (S&P 500).

```{r}
#| echo: false

##################### S&P 500

replaceCommas<-function(x){
  x<-as.numeric(gsub("\\,", "", x))
}

sp500_dat <- rio::import("https://byuistats.github.io/timeseries/data/sp500.csv") |>
  mutate(dates = mdy(Date))

sp500_day <- sp500_dat |>
  mutate(date_seq = dates) |>
  mutate(
    dates = date_seq,
    year = lubridate::year(date_seq),
    month = lubridate::month(date_seq),
    value = replaceCommas(Close)
  ) |>
  dplyr::select(-date_seq) |>
  tibble()

sp500_ts <- sp500_day |>
  mutate(index = dates) |>
  as_tsibble(index = index)

sp500_annual_ts <- summarise(index_by(sp500_ts, year), value = mean(value))

temp <- sp500_ts |> filter(month == 7 & day(dates) == 1) |> 
  dplyr::select(Date, year) 

temp2 <- sp500_annual_ts |> 
  right_join(temp, by = join_by(year))

autoplot(sp500_ts, .vars = value) +
  labs(
    x = "Date",
    y = "Closing Price",
    title = "Daily Closing Price of the S&P 500 Stock Index"
  )  +
  theme(plot.title = element_text(hjust = 0.5))
```

::: panel-tabset
#### Characteristics

#### Trend

The red line represents the mean for each year. The point for this line was positioned to align with July of the year.

```{r}
#| echo: false

##################### S&P 500

replaceCommas<-function(x){
  x<-as.numeric(gsub("\\,", "", x))
}

sp500_dat <- rio::import("https://byuistats.github.io/timeseries/data/sp500.csv") |>
  mutate(dates = mdy(Date))

sp500_day <- sp500_dat |>
  mutate(date_seq = dates) |>
  mutate(
    dates = date_seq,
    year = lubridate::year(date_seq),
    month = lubridate::month(date_seq),
    value = replaceCommas(Close)
  ) |>
  dplyr::select(-date_seq) |>
  tibble()

sp500_ts <- sp500_day |>
  mutate(index = dates) |>
  as_tsibble(index = index)

sp500_annual_ts <- summarise(index_by(sp500_ts, year), value = mean(value))

temp <- sp500_ts |> filter(month == 7 & day(dates) == 1) |> 
  dplyr::select(Date, year) 

temp2 <- sp500_annual_ts |> 
  right_join(temp, by = join_by(year))

autoplot(sp500_ts, .vars = value) +
  labs(
    x = "Date",
    y = "Closing Price",
    title = "Daily Closing Price of the S&P 500 Stock Index"
  )  +
  theme(plot.title = element_text(hjust = 0.5)) +
  # geom_line(data = temp2, 
  #           aes(x = index, y = value),
  #           color = "red") +
  geom_smooth(formula = y ~ x, method = "loess", color = "#D55E00")
```

:::: {.callout-tip icon=false title="Check Your Understanding"}

-   What do you observe about the value of the S&P 500 over time?
-   What might be causing this trend?

::::

#### Seasonality / Cycles

:::: {.callout-tip icon=false title="Check Your Understanding"}

-   Are there regularly-occurring seasonal trends in the data?
-   Are there some random (stochastic) business cycles observable in the data?
-   How can you explain these observations?

::::

#### Autocorrelation

:::: {.callout-tip icon=false title="Check Your Understanding"}

-   Consider closing prices in successive days. Are they independent?
-   Why would there be autocorrelation in the data?

::::

:::

Discuss these vocabulary terms in the context of the S&P 500 example: 

- Time series 
- Sampling interval 
- Autocorrelation (or serial dependence) 
- Trend 
- Seasonal variation 
- Cycle 
- Deterministic vs. Stochastic

## Recap (5 min)

-   What is time series data?
    -   Define "time series" (e.g. observations collected sequentially over time)
-   Examples of time series data
-   Why ordinary regression fails -- correlated error terms
-   Examples of time series from different domains:
    -   Daily credit card balance
    -   Daily closing stock prices
    -   Monthly sales figures
    -   Yearly global temperature measurements
    -   Secondly wave heights in an ocean buoy
    -   Weekly unemployment rates
    -   Quarterly GDP estimates
-   Importance of context and subject matter knowledge
-   Role of models (explanation, prediction, simulation)
-   Are there any questions on the course or time series data?


## Homework Preview (5 min)

-   Review upcoming homework assignment
-   Clarify questions


## Homework

::: {.callout-note icon=false}

## Download Assignment

<a href="https://byuistats.github.io/timeseries/homework/homework_1_1.qmd" download="homework_1_1.qmd"> homework_1_1.qmd </a>

## Preparation for the next class meeting

-   Update R and RStudio
-   Access
    -   Canvas course
    -   Time Series Notebook (Quarto file)
-   Purchase the textbook
-   Read sections 1.1-1.4 in the textbook
-   Obtain a Learning Journal
-   Prepare to share your Learning Journal with another student in the next class meeting

:::