TBATS models for electricity demand

As you saw in the video, a TBATS model is a special kind of time series model. It can be very slow to estimate, especially with multiple seasonal time series, so in this exercise you will try it on a simpler series to save time. Let's break down elements of a TBATS model in TBATS(1, {0,0}, -, {<51.18,14>}), one of the graph titles from the video:

Component	Meaning
1	Box-Cox transformation parameter
{0,0}	ARMA error
-	Damping parameter
{\<51.18,14>}	Seasonal period, Fourier terms

The gas data contains Australian monthly gas production. A plot of the data shows the variance has changed a lot over time, so it needs a transformation. The seasonality has also changed shape over time, and there is a strong trend. This makes it an ideal series to test the tbats() function which is designed to handle these features.

gas is available to use in your workspace.

Cet exercice fait partie du cours

Forecasting in R

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Instructions

Plot gas using the standard plotting function.
Fit a TBATS model using the newly introduced method to the gas data as fit.
Forecast the series for the next 5 years as fc.
Plot the forecasts of fc. Inspect the graph title by reviewing the table above.
Save the Box-Cox parameter to 3 decimal places and order of Fourier terms to lambda and K, respectively.

Exercice interactif pratique

Essayez cet exercice en complétant cet exemple de code.

# Plot the gas data
___(___)

# Fit a TBATS model to the gas data
fit <- ___(___)

# Forecast the series for the next 5 years
fc <- ___(___)

# Plot the forecasts
___(___)

# Record the Box-Cox parameter and the order of the Fourier terms
lambda <- ___
K <- ___

Modifier et exécuter le code

Cet exercice fait partie du cours

Forecasting in R

IntermédiaireNiveau de compétence

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

Exercice en cours

Exercise 10: Your future in forecasting!