Adattare un modello AR(2)

Per questo esercizio, abbiamo generato dati dal modello AR(2), $$X_t = 1.5 X_{t-1} - .75 X_{t-2} + W_t,$$ usando x <- arima.sim(model = list(order = c(2, 0, 0), ar = c(1.5, -.75)), n = 200). Osserva i dati simulati e la coppia ACF e PACF campionarie per determinare l'ordine del modello. Poi adatta il modello e confronta i parametri stimati con quelli reali.

Questo esercizio fa parte del corso

Modelli ARIMA in R

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Istruzioni dell'esercizio

Il pacchetto astsa è precaricato. x contiene le 200 osservazioni AR(2).
Usa plot() per tracciare i dati generati in x.
Traccia la coppia ACF e PACF campionarie usando acf2() dal pacchetto astsa.
Usa sarima() per adattare un AR(2) ai dati generati in x. Esamina la t-table e confronta le stime con i valori reali.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# astsa is preloaded

# Plot x


# Plot the sample P/ACF of x


# Fit an AR(2) to the data and examine the t-table

Modifica ed esegui il codice

Questo esercizio fa parte del corso

Modelli ARIMA in R

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You will investigate the nature of time series data and learn the basics of ARMA models that can explain the behavior of such data. You will learn the basic R commands needed to help set up raw time series data to a form that can be analyzed using ARMA models.

Exercise 1: First things first Exercise 2: Data play Exercise 3: Elements of time series Exercise 4: Stationarity and nonstationarity Exercise 5: Differencing Exercise 6: Detrending data Exercise 7: Dealing with trend and heteroscedasticity Exercise 8: Stationary time series: ARMA Exercise 9: Simulating ARMA models

You will discover the wonderful world of ARMA models and how to fit these models to time series data. You will learn how to identify a model, how to choose the correct model, and how to verify a model once you fit it to data. You will learn how to use R time series commands from the stats and astsa packages.

Exercise 1: Modelli AR e MA Exercise 2: Adattare un modello AR(1)Exercise 3: Adattare un modello AR(2)

Esercizio in corso

Exercise 4: Adattare un modello MA(1)Exercise 5: AR e MA insieme Exercise 6: Adattare un modello ARMA Exercise 7: Identifica un modello ARMA Exercise 8: Scelta del modello e analisi dei residui Exercise 9: Scelta del modello - I Exercise 10: Scelta del modello - II Exercise 11: Analisi dei residui - I Exercise 12: Analisi dei residui - II Exercise 13: ARMA al via

Now that you know how to fit ARMA models to stationary time series, you will learn about integrated ARMA (ARIMA) models for nonstationary time series. You will fit the models to real data using R time series commands from the stats and astsa packages.

Exercise 1: ARIMA - integrated ARMA Exercise 2: ARIMA - plug and play Exercise 3: Simulated ARIMA Exercise 4: Global warming Exercise 5: ARIMA diagnostics Exercise 6: Diagnostics - simulated overfitting Exercise 7: Diagnostics - global temperatures Exercise 8: Forecasting ARIMA Exercise 9: Forecasting simulated ARIMA Exercise 10: Forecasting global temperatures

You will learn how to fit and forecast seasonal time series data using seasonal ARIMA models. This is accomplished using what you learned in the previous chapters and by learning how to extend the R time series commands available in the stats and astsa packages.

Exercise 1: Pure seasonal models Exercise 2: P/ACF of pure seasonal models Exercise 3: Fit a pure seasonal model Exercise 4: Mixed seasonal models Exercise 5: Fit a mixed seasonal model Exercise 6: Data analysis - unemployment I Exercise 7: Data analysis - unemployment II Exercise 8: Data analysis - commodity prices Exercise 9: Data analysis - birth rate Exercise 10: Forecasting seasonal ARIMA Exercise 11: Forecasting monthly unemployment Exercise 12: How hard is it to forecast commodity prices?Exercise 13: Congratulations!