The asymptotic distribution of the sample inverse autocorrelations of an autoregressive-moving average process

Abstract

The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.