Previsioni delle prenotazioni di chiamate

Un'altra serie storica con stagionalità multiple è calls, che contiene 20 giorni consecutivi di dati sui volumi di chiamate a intervalli di 5 minuti per una grande banca nordamericana. Ci sono 169 intervalli da 5 minuti in un giorno lavorativo, quindi la frequenza stagionale settimanale è 5 x 169 = 845. La stagionalità settimanale è relativamente debole, quindi qui modellerai solo la stagionalità giornaliera. calls è già caricata nel tuo workspace.

In questo caso i residui non superano comunque i test di rumore bianco, ma le loro autocorrelazioni sono minuscole, anche se significative. Questo perché la serie è molto lunga. È spesso irrealistico avere residui che superano i test per serie così lunghe. L'effetto delle correlazioni rimanenti sulle previsioni sarà trascurabile.

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Previsioni in R

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Istruzioni dell'esercizio

Traccia i dati calls per vedere la forte stagionalità giornaliera e la debole stagionalità settimanale.
Imposta la matrice xreg usando l'ordine 10 per la stagionalità giornaliera e 0 per la stagionalità settimanale. Nota che, se specifichi il vettore in modo errato, la tua sessione potrebbe scadere!
Stima un modello di regressione dinamica chiamato fit usando auto.arima() con seasonal = FALSE e stationary = TRUE.
Controlla i residui del modello stimato.
Crea le previsioni per 10 giorni lavorativi in avanti come fc e poi tracciale. La descrizione dell'esercizio dovrebbe aiutarti a determinare il valore corretto di h.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# Plot the calls data
___

# Set up the xreg matrix
xreg <- fourier(___, K = ___)

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

# Check the residuals
___

# Plot forecasts for 10 working days ahead
fc <- forecast(fit, xreg =  fourier(calls, c(10, 0), h = ___))
___

Modifica ed esegui il codice

Questo esercizio fa parte del corso

Previsioni in R

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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

Esercizio in corso

Exercise 8: Modelli TBATS Exercise 9: Modelli TBATS per la domanda di elettricità Exercise 10: Il tuo futuro nel forecasting!