ASYMPTOTIC PROPERTIES OF SOME ESTIMATORS FOR PARTLY LINEAR STATIONARY AUTOREGRESSIVE MODELS

Consider the time series model y(t) = beta y(t-1) + g(y(t-2),...,y(t-p)) + e(t) for t greater than or equal to p +1. Here beta is an unknown parameter to be estimated, g(.) is an unknown function in R(p-1), e(t) are i.i.d. random errors with Ee(1) = 0 and Ee(1)(2) < infinity, and e(t) are independent of y(s) for all s = 1,2,..,p and t greater than or equal to p + 1. Based on a kernel estimate ($) over cap(T)(.) of g(.) and the model y(t) = beta y(t-1) + ($) over cap g(T)(y(t-2),...,y(t-p)) + e(1), we investigate the asymptotic normality of the least squares estimate beta ($) over cap(T) of beta and an estimate sigma ($) over cap T-2 of sigma(2), and obtain the law of the iterated logarithm for beta ($) over cap(T) and sigma ($) over cap(T)(2).