Rob J. Hyndman once wrote in "Why I don't like statistical tests" (emphasis is mine):

In forecasting, the only place in which I find testing useful is in determining the order of integration of a time series; i.e., choosing d in an ARIMA(p,d,q) model. If I could come up with some way of doing this effectively without using a unit-root test, I would gladly do so. But so far, I have not found a reliable alternative.

I know that AIC-based comparisons are tricky when models for different transformations of the data are considered; one needs to account for that using Jacobians or something like that -- I have never got my hands dirty with this, so I do not know precisely.

But are they prohibitively tricky? Or what is the reason for the lack of "reliable alternatives" above? What about the following AIC-based comparison to replace unit-root testing for model selection in forecasting: for a given time series $\{x_t\}_{t=1}^T$,

  1. Fit an ARIMA(1,0,0) model and obtain its likelihood for observations $t=2,\dots,T$
  2. Fit an ARIMA(0,1,0) model and obtain its likelihood for observations $t=2,\dots,T$ (not for $\Delta x_t$ but for $x_t$, of course)
  3. Construct AIC values for the two (which should be somehow tricky for case 2. -- or should it not?) and compare them.

(This is not supposed to be an alternative for testing the hypothesis of presence of a unit root. But I hope it could be an alternative in model selection.)



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.