Een AR(2)-model fitten

Voor deze oefening hebben we data gegenereerd uit het AR(2)-model, $$X_t = 1.5 X_{t-1} - .75 X_{t-2} + W_t,$$ met x <- arima.sim(model = list(order = c(2, 0, 0), ar = c(1.5, -.75)), n = 200). Bekijk de gesimuleerde data en het koppel van de steekproef-ACF en -PACF om de modelorde te bepalen. Fit daarna het model en vergelijk de geschatte parameters met de echte parameters.

Deze oefening maakt deel uit van de cursus

ARIMA-modellen in R

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Oefeninstructies

Het pakket astsa is vooraf geladen. x bevat de 200 AR(2)-waarnemingen.
Gebruik plot() om de gegenereerde data in x te plotten.
Plot het paar van de steekproef-ACF en -PACF met acf2() uit het astsa-pakket.
Gebruik sarima() om een AR(2) te fitten op de eerder gegenereerde data in x. Bekijk de t-tabel en vergelijk de schattingen met de echte waarden.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# astsa is preloaded

# Plot x


# Plot the sample P/ACF of x


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

Code bewerken en uitvoeren

Deze oefening maakt deel uit van de cursus

ARIMA-modellen 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: AR- en MA-modellen Exercise 2: Een AR(1)-model fitten Exercise 3: Een AR(2)-model fitten

Huidige oefening

Exercise 4: Een MA(1)-model passen Exercise 5: AR en MA samen Exercise 6: Een ARMA-model fitten Exercise 7: Identificeer een ARMA‑model Exercise 8: Modelkeuze en residu-analyse Exercise 9: Modelkeuze - I Exercise 10: Modelkeuze - II Exercise 11: Residualanalyse - I Exercise 12: Residuanalyse - II Exercise 13: ARMA, kom d'r in

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!