Prevedere la domanda di elettricità

Puoi anche modellare la domanda giornaliera di elettricità in funzione della temperatura. Come avrai notato sulla bolletta, si consuma più elettricità nei giorni caldi per l’aria condizionata e nei giorni freddi per il riscaldamento.

In questo esercizio, adatterai un modello di regressione quadratica con errore ARMA. Un anno di dati giornalieri è memorizzato in elecdaily e include la domanda totale giornaliera, una variabile indicatrice per i giorni lavorativi (un giorno lavorativo è rappresentato con 1, un giorno non lavorativo con 0) e le temperature massime giornaliere. Poiché c’è stagionalità settimanale, la frequency è stata impostata a 7.

Diamo un’occhiata alle prime tre righe:

> elecdaily[1:3, ]
       Demand Temperature Workday
[1,] 174.8963        26.0       0
[2,] 188.5909        23.0       1
[3,] 188.9169        22.2       1

elecdaily è stato caricato in anticipo nel tuo workspace.

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Istruzioni dell'esercizio

Produci i grafici temporali di sole la domanda giornaliera e delle temperature massime con facetting.
Prepara una matrice di regressori includendo MaxTemp per le temperature massime, MaxTempSq, che rappresenta il valore al quadrato della temperatura massima, e Workday, in quest’ordine. Chiaramente, il secondo argomento di cbind() richiederà un semplice operatore matematico.
Adatta un modello di regressione dinamica della colonna della domanda con errori ARIMA e chiamalo fit.
Se il giorno successivo è lavorativo (indicatore 1) con temperatura massima prevista di 20°C, qual è la domanda prevista? Compila i valori appropriati in cbind() per l’argomento xreg in forecast().

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# Time plots of demand and temperatures
autoplot(elecdaily[, c(___, ___)], facets = ___)

# Matrix of regressors
xreg <- cbind(MaxTemp = elecdaily[, "Temperature"],
              MaxTempSq = ___,
              Workday = ___)

# Fit model
fit <- auto.arima(___, xreg = xreg)

# Forecast fit one day ahead
forecast(___, xreg = cbind(___, ___, ___))

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

Esercizio in corso

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 Exercise 10: Il tuo futuro nel forecasting!