Exercise

Model choice - I

Based on the sample P/ACF pair of the logged and differenced varve data (dl_varve), an MA(1) was indicated. The best approach to fitting ARMA is to start with a low order model, and then try to add a parameter at a time to see if the results change.

In this exercise, you will fit various models to the dl_varve data and note the AIC and BIC for each model. In the next exercise, you will use these AICs and BICs to choose a model. Remember that you want to retain the model with the smallest AIC and/or BIC value.

A note before you start:

sarima(x, p = 0, d = 0, q = 1) and sarima(x, 0, 0, 1)

are the same.

Instructions

100 XP
  • The package astsa is preloaded. The varve series has been logged and differenced as dl_varve <- diff(log(varve)).
  • Use sarima() to fit an MA(1) to dl_varve. Take a close look at the output of your sarima() command to see the AIC and BIC for this model.
  • Repeat the previous exercise, but add an MA parameter by fitting an MA(2) model. Based on AIC and BIC, is this an improvement over the previous model?
  • Instead of adding an MA parameter, add an AR parameter to the original MA(1) fit. That is, fit an ARMA(1,1) to dl_varve. Based on AIC and BIC, is this an improvement over the previous models?