Properties of the sample variance in samples from a generalised autoregressive scheme

Abstract

An attempt is made to study the properties of the sample variance in samples from a generalised autoregressive scheme, by computing the moments. Eventhough the expressions are lengthy, the moments can be derived. For the simple particular case xt = et -j- a.et , the moments have been worked out. The exact distribution has not been derived, but the large sample approximation is found to be normal with mean S2 (1 + a2) and variance (2/n) (a4 + 8a2 -f2).S4 When a ^ 0, s2 is a biased of S2.