Gesimuleerde ARIMA

Voordat je echte tijdreeksgegevens gaat analyseren, is het goed om met een iets ingewikkelder model te oefenen.

Hier hebben we 250 observaties gegenereerd uit het ARIMA(2,1,0)-model met drift, gegeven door $$Y_t = 1 + 1.5 Y_{t-1} - .75 Y_{t-2} + W_t\,$$ waarbij \(Y_t = \nabla X_t = X_{t} - X_{t-1}\).

Je gaat de bekende technieken gebruiken om een model op de gegevens te fitten.

Het pakket astsa is vooraf geladen en de gegenereerde gegevens staan in x. De reeks x en de gedifferentieerde reeks y <- diff(x) zijn al geplot.

Deze oefening maakt deel uit van de cursus

ARIMA-modellen in R

Cursus bekijken

Oefeninstructies

Plot de steekproef-ACF en -PACF met acf2() van de gedifferentieerde gegevens diff(x) om een model te bepalen.
Fit een ARIMA(2,1,0)-model met sarima() op de gegenereerde gegevens. Bekijk de t-tabel en andere uitvoerinformatie om de model-fit te beoordelen.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Plot sample P/ACF of differenced data and determine model



# Estimate parameters and examine output

Code bewerken en uitvoeren

Deze oefening maakt deel uit van de cursus

ARIMA-modellen in R

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Begin de cursus gratis

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 and MA models Exercise 2: Fitting an AR(1) model Exercise 3: Fitting an AR(2) model Exercise 4: Fitting an MA(1) model Exercise 5: AR and MA together Exercise 6: Fitting an ARMA model Exercise 7: Identify an ARMA model Exercise 8: Model choice and residual analysis Exercise 9: Model choice - I Exercise 10: Model choice - II Exercise 11: Residual analysis - I Exercise 12: Residual analysis - II Exercise 13: ARMA get 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 - geïntegreerde ARMA Exercise 2: ARIMA - plug-and-play Exercise 3: Gesimuleerde ARIMA

Huidige oefening

Exercise 4: Opwarming van de aarde Exercise 5: ARIMA-diagnostiek Exercise 6: Diagnostiek - gesimuleerde overfitting Exercise 7: Diagnostiek - mondiale temperaturen Exercise 8: ARIMA-voorspellingen Exercise 9: Voorspellen met gesimuleerde ARIMA Exercise 10: Wereldwijde temperaturen voorspellen

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!