Tests for fourth order autoregressive processes.

Abstract

Upper and lower bounds were determined for a variation of Schmidt's statistic using Imhoff's distribution for quadratic forms in normal variables. This statistic is able to detect a fourth order autoregressive disturbance of the form: Ɛ(ʈ)=ƿ(1)Ɛ(ʈ-1)+ƿ(4)Ɛ(ʈ-4)+ƞ(ʈ) in the general model Y=Xβ+Ɛ. To correct for this disturbance and thus yield efficient regression estimates, a data transformation was derived using the inverse of the variance-covariance matrix as defined by Siddiqui.