Seasonal plots

Along with time plots, there are other useful ways of plotting data to emphasize seasonal patterns and show changes in these patterns over time.

A seasonal plot is similar to a time plot except that the data are plotted against the individual “seasons” in which the data were observed. You can create one using the ggseasonplot() function the same way you do with autoplot().
An interesting variant of a season plot uses polar coordinates, where the time axis is circular rather than horizontal; to make one, simply add a polar argument and set it to TRUE.
A subseries plot comprises mini time plots for each season. Here, the mean for each season is shown as a blue horizontal line.

One way of splitting a time series is by using the window() function, which extracts a subset from the object x observed between the times start and end.

> window(x, start = NULL, end = NULL)

In this exercise, you will load the fpp2 package and use two of its datasets:

a10 contains monthly sales volumes for anti-diabetic drugs in Australia. In the plots, can you see which month has the highest sales volume each year? What is unusual about the results in March and April 2008?
ausbeer which contains quarterly beer production for Australia. What is happening to the beer production in Quarter 4?

These examples will help you to visualize these plots and understand how they can be useful.

This is a part of the course

“Forecasting in R”

Exercise instructions

Use library() to load the fpp2 package.
Use autoplot() and ggseasonplot() to produce plots of the a10 data.
Use the ggseasonplot() function and its polar argument to produce a polar coordinate plot for the a10 data.
Use the window() function to consider only the ausbeer data starting from 1992.
Finally, use autoplot() and ggsubseriesplot() to produce plots of the beer series.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Load the fpp2 package
___

# Create plots of the a10 data
___
___

# Produce a polar coordinate season plot for the a10 data
ggseasonplot(___, polar = ___)

# Restrict the ausbeer data to start in 1992
beer <- ___(___, ___)

# Make plots of the beer data
___
___

Edit and Run Code

This exercise is part of the course

Forecasting in R

IntermediateSkill Level

4.9+

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The first thing to do in any data analysis task is to plot the data. Graphs enable many features of the data to be visualized, including patterns, unusual observations, and changes over time. The features that are seen in plots of the data must then be incorporated, as far as possible, into the forecasting methods to be used.

Exercise 1: Welcome to Forecasting Using R Exercise 2: Creating time series objects in R Exercise 3: Time series plots Exercise 4: Seasonal plots

Exercise 5: Trends, seasonality, and cyclicity Exercise 6: Autocorrelation of non-seasonal time series Exercise 7: Autocorrelation of seasonal and cyclic time series Exercise 8: Match the ACF to the time series Exercise 9: White noise Exercise 10: Stock prices and white noise

In this chapter, you will learn general tools that are useful for many different forecasting situations. It will describe some methods for benchmark forecasting, methods for checking whether a forecasting method has adequately utilized the available information, and methods for measuring forecast accuracy. Each of the tools discussed in this chapter will be used repeatedly in subsequent chapters as you develop and explore a range of forecasting methods.

Exercise 1: Forecasts and potential futures Exercise 2: Naive forecasting methods Exercise 3: Fitted values and residuals Exercise 4: Checking time series residuals Exercise 5: Training and test sets Exercise 6: Evaluating forecast accuracy of non-seasonal methods Exercise 7: Evaluating forecast accuracy of seasonal methods Exercise 8: Do I have a good forecasting model?Exercise 9: Time series cross-validation Exercise 10: Using tsCV() for time series cross-validation

Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation, the higher the associated weight. This framework generates reliable forecasts quickly and for a wide range of time series, which is a great advantage and of major importance to applications in business.

Exercise 1: Exponentially weighted forecasts Exercise 2: Simple exponential smoothing Exercise 3: SES vs naive Exercise 4: Exponential smoothing methods with trend Exercise 5: Holt's trend methods Exercise 6: Exponential smoothing methods with trend and seasonality Exercise 7: Holt-Winters with monthly data Exercise 8: Holt-Winters method with daily data Exercise 9: State space models for exponential smoothing Exercise 10: Automatic forecasting with exponential smoothing Exercise 11: ETS vs seasonal naive Exercise 12: Match the models to the time series Exercise 13: When does ETS fail?

ARIMA models provide another approach to time series forecasting. Exponential smoothing and ARIMA models are the two most widely-used approaches to time series forecasting, and provide complementary approaches to the problem. While exponential smoothing models are based on a description of the trend and seasonality in the data, ARIMA models aim to describe the autocorrelations in the data.

Exercise 1: Transformations for variance stabilization Exercise 2: Box-Cox transformations for time series Exercise 3: Non-seasonal differencing for stationarity Exercise 4: Seasonal differencing for stationarity Exercise 5: ARIMA models Exercise 6: Automatic ARIMA models for non-seasonal time series Exercise 7: Forecasting with ARIMA models Exercise 8: Comparing auto.arima() and ets() on non-seasonal data Exercise 9: Seasonal ARIMA models Exercise 10: Automatic ARIMA models for seasonal time series Exercise 11: Exploring auto.arima() options Exercise 12: Comparing auto.arima() and ets() on seasonal data

The time series models in the previous chapters work well for many time series, but they are often not good for weekly or hourly data, and they do not allow for the inclusion of other information such as the effects of holidays, competitor activity, changes in the law, etc. In this chapter, you will look at some methods that handle more complicated seasonality, and you consider how to extend ARIMA models in order to allow other information to be included in the them.

Exercise 1: Dynamic regression Exercise 2: Forecasting sales allowing for advertising expenditure Exercise 3: Forecasting electricity demand Exercise 4: Dynamic harmonic regression Exercise 5: Forecasting weekly data Exercise 6: Harmonic regression for multiple seasonality Exercise 7: Forecasting call bookings Exercise 8: TBATS models Exercise 9: TBATS models for electricity demand Exercise 10: Your future in forecasting!