I have GDP Time series, that has a positive stochastic trend trend:
> CADFtest(logGDP, type= "trend", criterion= "BIC", max.lag.y=max.lag) > ADF test data: logGDP ADF(3) = -2.5019, p-value = 0.327
and is stationary:
> CADFtest(dlogGDP, type = "drift", criterion= "BIC", max.lag.y=max.lag) > ADF test data: dlogGDP ADF(1) = -5.963, p-value = 5.686e-07
The problem: There is some obvious heteroscedasticity in the data. I have removed the data from 19670-1992, reasoning that there has been structural change. I have fit
ARIMA (1,1,1) model and used the Q-test to validate it - the residuals are white noise. Is this correct?
Alternatively, I have tried to fit the ARCH and GARCH model on the entire time seties (1972 - 2015). ARCH has not yield an parsimonious model, based on the the correlogram of squared errors. I then fit a GARCH model and validated it.
- Which procedure is better/ more correct?
- Is there a way to compare the ARIMA model and GARCH model? How can I compare their performance?
- Are both models equally good for prediction?