Modelli TBATS per la domanda di elettricità

Come hai visto nel video, un modello TBATS è un tipo speciale di modello per serie temporali. Può essere molto lento da stimare, soprattutto con serie con stagionalità multiple; quindi in questo esercizio lo proverai su una serie più semplice per risparmiare tempo. Analizziamo gli elementi di un modello TBATS in TBATS(1, {0,0}, -, {<51.18,14>}), uno dei titoli dei grafici nel video:

Componente	Significato
1	Parametro di trasformazione Box-Cox
{0,0}	Errore ARMA
-	Parametro di smorzamento
{\<51.18,14>}	Periodo stagionale, termini di Fourier

I dati gas contengono la produzione mensile di gas in Australia. Un grafico dei dati mostra che la varianza è cambiata molto nel tempo, quindi serve una trasformazione. Anche la stagionalità ha cambiato forma nel tempo ed è presente un forte trend. Questo rende la serie ideale per testare la funzione tbats() progettata per gestire queste caratteristiche.

gas è disponibile nel tuo workspace.

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Istruzioni dell'esercizio

Rappresenta gas usando la funzione di plotting standard.
Adatta ai dati gas un modello TBATS con il metodo appena introdotto e salvalo in fit.
Prevedi la serie per i prossimi 5 anni e salva il risultato in fc.
Traccia il grafico delle previsioni di fc. Controlla il titolo del grafico confrontandolo con la tabella qui sopra.
Salva il parametro di Box-Cox con 3 cifre decimali e l'ordine dei termini di Fourier in lambda e K, rispettivamente.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# 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 <- ___

Modifica ed esegui il codice

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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: Regressione dinamica Exercise 2: Prevedere le vendite tenendo conto della spesa pubblicitaria Exercise 3: Prevedere la domanda di elettricità Exercise 4: Regressione armonica dinamica Exercise 5: Previsioni con dati settimanali Exercise 6: Regressione armonica per stagionalità multiple Exercise 7: Previsioni delle prenotazioni di chiamate Exercise 8: Modelli TBATS Exercise 9: Modelli TBATS per la domanda di elettricità

Esercizio in corso

Exercise 10: Il tuo futuro nel forecasting!