Autocorrelatie van niet-seizoensgebonden tijdreeksen

Een andere manier om naar tijdreeksdata te kijken is door elke observatie uit te zetten tegen een eerdere observatie met gglagplot(). Je kunt bijvoorbeeld \(y_t\) uitzetten tegen \(y_{t-1}\). Dit heet een lag-plot, omdat je de tijdreeks uitzet tegen vertragingen (lags) van zichzelf.

De correlaties die bij de lag-plots horen vormen wat de autocorrelatiefunctie (ACF) wordt genoemd. De functie ggAcf() maakt ACF-plots.

In deze oefening werk je met de vooraf geladen oil-data (beschikbaar in het pakket fpp2), die de jaarlijkse olieproductie in Saoedi-Arabië van 1965–2013 bevat (gemeten in miljoenen ton).

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Gebruik de functie autoplot() om de oil-data te plotten.
Plot voor de oil-data de relatie tussen \(y_t\) en \(y_{t-k}\), \(k=1,\dots,9\) met een van de twee zojuist geïntroduceerde functies. Kijk hoe de relaties veranderen als de vertraging toeneemt.
Plot op dezelfde manier de correlaties die bij elk van de lag-plots horen met de andere geschikte nieuwe functie.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Create an autoplot of the oil data
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# Create a lag plot of the oil data
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# Create an ACF plot of the oil data
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Code bewerken en uitvoeren

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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: Welkom bij Forecasting met R Exercise 2: Tijdreeksobjecten maken in R Exercise 3: Tijdreeksplots Exercise 4: Seizoensplots Exercise 5: Trends, seizoenspatronen en cycliciteit Exercise 6: Autocorrelatie van niet-seizoensgebonden tijdreeksen

Huidige oefening

Exercise 7: Autocorrelatie van seizoens- en cyclische tijdreeksen Exercise 8: Koppel de ACF aan de tijdreeks Exercise 9: Witte ruis Exercise 10: Aandelenkoersen en witte ruis

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 Exercise 10: Your future in forecasting!