Smussamento esponenziale semplice

La funzione ses() genera previsioni ottenute usando il simple exponential smoothing (SES), ovvero lo smussamento esponenziale semplice. I parametri vengono stimati con il metodo dei minimi quadrati. Devi solo specificare la serie temporale e l’orizzonte di previsione; l’orizzonte predefinito è h = 10 anni.

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

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

Userai anche summary() e fitted(), insieme a autolayer() per la prima volta, che è simile a autoplot() ma aggiunge un "layer" a un grafico invece di crearne uno nuovo.

Qui applicherai queste funzioni a marathon, i tempi annuali dei vincitori della maratona di Boston dal 1897 al 2016. I dati sono disponibili nel tuo workspace.

Questo esercizio fa parte del corso

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Istruzioni dell'esercizio

Usa la funzione ses() per prevedere i tempi vincenti dei prossimi 10 anni.
Usa la funzione summary() per vedere i parametri del modello e altre informazioni.
Usa la funzione autoplot() per tracciare le previsioni.
Aggiungi al grafico le previsioni a un passo per i dati di training, ovvero i valori adattati, usando fitted() e autolayer().

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# 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(___))

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: Previsioni a pesi esponenziali Exercise 2: Smussamento esponenziale semplice

Esercizio in corso

Exercise 3: SES vs naive Exercise 4: Metodi di smoothing esponenziale con trend Exercise 5: Metodi di trend di Holt Exercise 6: Metodi di smoothing esponenziale con trend e stagionalità Exercise 7: Holt-Winters con dati mensili Exercise 8: Metodo di Holt-Winters con dati giornalieri Exercise 9: Modelli a spazio degli stati per lo smoothing esponenziale Exercise 10: Previsioni automatiche con lo smoothing esponenziale Exercise 11: ETS vs naive stagionale Exercise 12: Abbina i modelli alle serie temporali Exercise 13: Quando ETS fallisce?

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!