Asymptotic Properties Of Some Estimators In Moving Average Models PDF Download

The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k> or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix with equal elements along its five central diagonals, and zeroes elsewhere. The asymptotic normality follows from a central limit theorem for normalized sums of random variables that are dependent of order k, where k tends to infinity with T. An alternative form of the estimator facilitates the calculations and the analysis of the role of k, without changing the asymptotic properties.