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.
This exercise is part of the course
ARIMA Models in R
Exercise instructions
- The package astsa is preloaded. The
varve
series has been logged and differenced asdl_varve <- diff(log(varve))
. - Use
sarima()
to fit an MA(1) todl_varve
. Take a close look at the output of yoursarima()
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?
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Fit an MA(1) to dl_varve.
# Fit an MA(2) to dl_varve. Improvement?
# Fit an ARMA(1,1) to dl_varve. Improvement?