LEAST SQUARES ESTIMATES AND ORDER DETERMINATION PROCEDURES FOR AUTOREGRESSIVE PROCESSES WITH A TIME DEPENDENT VARIANCE

Abstract

Abstract. We study nonstationary autoregressive processes, where the variance of the generating white noise process is allowed to depend on time. It is shown that ordinary least squares estimates are strongly consistent and with a proper scaling factor asymptotically normal, but, as can be expected, they are not efficient. Furthermore, AIC type order determination criteria, used as if the underlying process is stationary, are consistent, whereas identification of order in terms of the partial autocorrelation function may lead one astray.