Abstract
Consider the following two types of moving average models; Model (1) Xt=et+αet-1 and Model (2) Xt=αet+et-1, where |α|<1 and et; t=0, ±1, …, are i. i. d. (0, σ2) random variables with the third-order cumulant c3. If c3≠0, it is known that the Models (1) and (2) are identifiable from {Xt}.
In this paper we propose a linear discriminant function, ξn, based on the third-order moments of {Xt}, which has a certain optimal property. Using ξn we give a method to discriminate between the Models (1) and (2). Numerical studies are given, and they are found to confirm the theoretical results.
