51  Exploratory Time Series Analysis - Practical

51.1 Introduction

The previous section on Exploratory TSA covered a lot of ground.

We’ll break this down into short stages in today’s practical session. This session will cover very basic concepts only.

51.2 Time series analysis: demonstration

Step One: Preparation

First, I’ll load some libraries.

rm(list=ls()) # clear environment

# Load necessary libraries
library(ggplot2)
library(forecast)
library(tseries)

For this demonstration I’m going to create an artificial dataset with two variables: Week and Speed. This represents the average speed a runner has achieved during training each week for a full year.

Show code for data creation 
# Average running speed of an athlete over 52 weeks
set.seed(123) # For reproducibility
weeks <- 1:52
speed <- round(10 + rnorm(52, mean = 0, sd = 0.4),2) # Average speed with some random variation
sports_data <- data.frame(Week = weeks, Speed = speed)
rm(speed)
rm(weeks)

head(sports_data)
  Week Speed
1    1  9.78
2    2  9.91
3    3 10.62
4    4 10.03
5    5 10.05
6    6 10.69

So we have one observation (Speed) for each Week that has been observed.

We can say this is a time series because it a regular capture of information on a consistent time frame.

In order to take advantage of the specific features of TSA, we need to tell R that the data is actually in the form of a time series.

Step Two: Creating a time series object

So, we convert the dataframe sports_data to a time series format.

If we don’t do this, R won’t know that it’s a time series, and we will not be able to use specialised TSA functions to examine the important features of such data (such as seasonality, or periodicity).

This is critical, and worth taking some time to examine.

In a previous section, we introduced the ts command, which lets us tell R our data is a time series.

We’ll stick with the simplest form for now, which is ts(data, frequency). If you want to go further into this, you’ll find that you can create start and end dates as well.

  • In this code, data represents the numerical data you want to convert into a time series. In our case, it’s the Speed variable.

  • The frequency is number of observations per unit of time. For example, 12 for monthly data in a year, 4 for quarterly data, etc.

It’s important to understand how this works: we’re telling R how many observations we have for one year.

In our case, the data is weekly, so we enter 52 as frequency (and sports_data$Speed as our data).

# Convert to time series using the ts function
ts_data <- ts(sports_data$Speed, frequency = 52)

We can now plot this time series as follows. Note that I’ve added a simple moving average in red to help simplify the data. Also, notice that R has understood that each observation represents a weekly time period (with week one = 1.0, and week 52 = 1.9).

library(ggplot2)
library(zoo)

Attaching package: 'zoo'
The following objects are masked from 'package:base':

    as.Date, as.Date.numeric
# Convert time series to data frame
ts_df <- data.frame(Time = time(ts_data), Value = as.vector(ts_data))

# Calculate the moving average
ts_df$MovingAvg <- rollmean(ts_df$Value, k = 12, fill = NA, align = "center")

# Plot using ggplot2
ggplot(ts_df, aes(x = Time)) + 
  geom_line(aes(y = Value), color = "blue") +  # Original time series
  geom_line(aes(y = MovingAvg), color = "red") +  # Moving average
  labs(x = "Time", y = "Value", title = "Time Series with Moving Average") +
  theme_minimal()
Don't know how to automatically pick scale for object of type <ts>. Defaulting
to continuous.
Warning: Removed 11 rows containing missing values or values outside the scale range
(`geom_line()`).

When creating time series data in R, I tend to think of the ‘big period’ and the ‘little period’. In this case, big period was a year, and little period was a week.

Imagine our data had been collected differently. Let’s say we had collected 52 observations, but instead of one per week, we’d collected five per week.

In this case, our ‘big period’ would be the week, and our ‘little period’ how many observations we have per week (5).

We’d create our time-series object like this:

# Convert to time series

ts_data_02 <- ts(sports_data$Speed, frequency = 5)

In this case, we’ve told our object that there are 5 observations per time period (i.e., 5 observations per week, or ‘big period’). Remember: our object doesn’t care what the period is…it just needs to know how many observations are in each period.

A plot of that data would look like this:

Show code 
# Plotting the time series with 'Week' on the x-axis
plot(ts_data_02, type = "o", col = "blue", main = "Five Observations per Week", xlab = "Week", ylab = "Value")


# Apply a simple moving average
# Calculate the moving average over a window of 12 periods
moving_avg <- rollmean(ts_data_02, k = 10, fill = NA, align = "center")
lines(moving_avg, col="red")

# for clarity, I've added a vertical line at each week
for(i in seq(1, length(ts_data_02), by = 1)) {
  abline(v = i, col = "gray", lty = 2)
}

Note that it’s exactly the same! The only thing that’s changed is that we’ve specified our final time point as being 12 rather than 52, and that there are 5 observations per time period rather than 52.

This highlights the importance of having equal numbers of observations per time period. It wouldn’t work (well it could but we’re keeping it simple) if you had three observations one week, and six the next.

So we have covered the idea of creating a time-series dataset that can now be explored using specific techniques designed for such data.

51.3 Time series analysis: practice

Based on the steps outlined above, conduct a basic time series analysis for the dataset df that is available here:

df <- read.csv('https://www.dropbox.com/scl/fi/nh221nxwv0fp0fy773i2j/golf_data.csv?rlkey=666lxnhwazjpg70j9wgowog8x&dl=1')
df <- df[1:156,]
df$Date <- NULL
df$Score <- round(df$Score,0)

The dataset contains data gathered from a golfer who has recorded their average score for per week over a period of three years.

Notes:

  • Create an appropriate time-series object for the data.

  • Don’t ignore descriptive statistics and exploratory data analysis - these should be your first stages regardless of what you’re going to do next.

  • Focus on interpreting visual plots, as well as statistical output.

  • Be ready to report your findings regarding seasonality in the data.

  • Crucially, did the golfer perform better in certain seasons than others?

  • What was the overall trend in their performance over time?

show solution 
# Convert to time series

golf_data <- ts(df$Score, frequency = 52)

# Plotting time series
plot(golf_data, type = "o", col = "blue", main = "Average Score per Week", xlab = "Year", ylab = "Av Score")


# Apply a simple moving average
# Calculate the moving average over a window of 12 periods
moving_avg <- rollmean(golf_data, k = 10, fill = NA, align = "center")
lines(moving_avg, col="red")

# for clarity, I've added a vertical line at each year
for(i in seq(1, length(golf_data), by = 1)) {
  abline(v = i, col = "gray", lty = 2)
}

show solution 
# Time Series Decomposition
decomposed <- stl(golf_data, s.window = "periodic")
plot(decomposed)