1

Suppose I have a set of economic time series that appear to be a unit root process. I difference them, and fit an ARMA model to the differenced series. Suppose however that the true data generating process is integrated not of order 1, but of order d, for 1 < d < 1.5, i.e I am estimating a misspecified model.

Let us say that I am doing short-term forecasts, only a few periods ahead. I would like it to be true that the fractional (d – 1) part of the integration is either negligible over this short time horizon or is absorbed into the AR or MA coefficients to the extent that it matters, such that the coefficient values may be wrong, but the short-term forecasts will nonetheless be right.

Should I expect this outcome? Or is this misspecification more serious than that, even in the short term?

andrewH
  • 2,587
  • 14
  • 27
  • Intuitively, I think you are right. In the short run, ARIMA should approximate ARFIMA well. But I don't know if there are any theoretical results on the topic. There could well be, perhaps you just need a clever search strategy (5 minutes of my searching did not result in anything relevant). Or you could reformulate the question slightly and tag it with [tag:references] and/or [tag:proof] asking for theoretical results on approximations of ARFIMA with ARIMA. – Richard Hardy May 02 '20 at 10:49

0 Answers0