Eenvoudige exponentiële afvlakking

De functie ses() maakt voorspellingen met simple exponential smoothing (SES). De parameters worden geschat met kleinste-kwadraten. Je hoeft alleen de tijdreeks en de voorspellingshorizon op te geven; de standaard voorspellingshorizon is h = 10 jaar.

> args(ses)
function (y, h = 10, ...)

> fc <- ses(oildata, h = 5)
> summary(fc)

Je gebruikt ook summary() en fitted(), en voor het eerst autolayer(). Dat lijkt op autoplot(), maar voegt een "laag" toe aan een bestaande plot in plaats van een nieuwe plot te maken.

Hier pas je deze functies toe op marathon, de jaarlijkse winnende tijden van de Boston Marathon van 1897–2016. De gegevens staan klaar in je werkruimte.

Deze oefening maakt deel uit van de cursus

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Oefeninstructies

Gebruik de functie ses() om de winnende tijden voor de komende 10 jaar te voorspellen.
Gebruik de functie summary() om de modelparameters en andere informatie te bekijken.
Gebruik de functie autoplot() om de voorspellingen te plotten.
Voeg de éénstapsvoorspellingen voor de trainingsdata, oftewel de gefitte waarden, toe aan de plot met fitted() en autolayer().

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Use ses() to forecast the next 10 years of winning times
fc <- ___(___, h = ___)

# Use summary() to see the model parameters
___

# Use autoplot() to plot the forecasts
___

# Add the one-step forecasts for the training data to the plot
autoplot(___) + autolayer(fitted(___))

Code bewerken en uitvoeren

Deze oefening maakt deel uit van de cursus

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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: Exponentieel gewogen voorspellingen Exercise 2: Eenvoudige exponentiële afvlakking

Huidige oefening

Exercise 3: SES vs naive Exercise 4: Exponentiële gladstrijkmethoden met trend Exercise 5: Trendomethoden van Holt Exercise 6: Exponentiële-smoothingmethoden met trend en seizoenspatroon Exercise 7: Holt-Winters met maandelijkse data Exercise 8: Holt-Winters-methode met dagelijkse data Exercise 9: Toestandsruimtemodellen voor exponentiële afvlakking Exercise 10: Automatisch voorspellen met exponentiële afvlakking Exercise 11: ETS versus seizoensgebonden naïef Exercise 12: Koppel de modellen aan de tijdreeksen Exercise 13: Wanneer faalt ETS?

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!