Statistical inference for a random coefficient autoregressive model

Abstract

A first-order autoregressive (AR(1)) model is considered, involving a coefficient that is a random variable, and may vary over realizations. In the usual AR(1) model the coefficient has a degenerate distribution, and is thus constant over realizations. We show how moments of the coefficient can be identified in terms of the autocovariances. Using mixed cross-section and time series data, we show how the moments can be estimated, and establish the strong consistency and asymptotic normality of the estimators. We suggest several parametric forms for the distribution of the coefficient, and show how unknown parameters may be determined. The results are applied to real data.