Reserveringen voor telefoontjes voorspellen

Een andere tijdreeks met meerdere seizoensperioden is calls, met 20 opeenvolgende dagen aan 5‑minutenbelvolumedata voor een grote Noord-Amerikaanse bank. Er zijn 169 5‑minutenintervallen op een werkdag, dus de wekelijkse seizoensfrequentie is 5 x 169 = 845. De wekelijkse seizoensinvloed is relatief zwak, dus je modelleert hier alleen dagelijkse seizoensinvloeden. calls is alvast in je werkruimte geladen.

De residuen slagen in dit geval nog steeds niet voor de white-noise-tests, maar hun autocorrelaties zijn heel klein, ook al zijn ze significant. Dat komt doordat de reeks zo lang is. Voor zulke lange reeksen is het vaak niet realistisch om residuen te hebben die voor alle tests slagen. Het effect van de overblijvende correlaties op de voorspellingen is verwaarloosbaar.

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Plot de calls-data om de sterke dagelijkse en zwakke wekelijkse seizoensinvloeden te zien.
Stel de xreg-matrix in met orde 10 voor dagelijkse seizoensinvloeden en 0 voor wekelijkse seizoensinvloeden. Let op: als je je vector onjuist opgeeft, kan je sessie verlopen!
Pas een dynamisch regressiemodel fit met auto.arima() toe met seasonal = FALSE en stationary = TRUE.
Controleer de residuen van het gefitte model.
Maak de voorspellingen voor 10 werkdagen vooruit als fc en plot deze vervolgens. De beschrijving van de oefening helpt je de juiste waarde van h te bepalen.

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Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# 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 = ___))
___

Code bewerken en uitvoeren

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Voorspellen 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: Dynamische regressie Exercise 2: Verkopen voorspellen met advertentiebudget als verklarende variabele Exercise 3: Electriciteitsvraag voorspellen Exercise 4: Dynamische harmonische regressie Exercise 5: Wekelijkse data voorspellen Exercise 6: Harmonische regressie voor meerdere seizoenspatronen Exercise 7: Reserveringen voor telefoontjes voorspellen

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Exercise 8: TBATS-modellen Exercise 9: TBATS-modellen voor elektriciteitsvraag Exercise 10: Jouw toekomst in forecasting!