Two-Stage Weighted Least Squares Estimation of Nonstationary Random Coefficient Autoregressions

Abstract

AbstractThis paper proposes a two-stage weighted least squares (2S-WLS) estimate for the autoregressive parameter and the random coefficient variance of a non-(strictly) stationary random coefficient autoregression (RCA). In the first stage, the autoregressive parameter is estimated from the conditional mean equation by a weighted least squares (WLS) method in which the weight is the conditional variance evaluated at any arbitrary known parameter value. In the second stage, based on the estimated conditional variance equation, the random coefficient variance is estimated again using the WLS method, but weighted by the squared conditional variance arbitrarily evaluated. It will be shown that the 2S-WLS estimate is asymptotically Gaussian with the same asymptotic variance as the quasi-maximum likelihood estimate under very mild conditions. Applications to the Gaussian double autoregression and the Markov bilinear model are given.