Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models

Abstract:     
The aim of this work is to investigate the asymptotic properties of weighted least squares (WLS) estimation for causal and invertible periodic autoregressive moving average (PARMA) models with uncorrelated but dependent errors. Under mild assumptions, it is shown that the WLS estimators of PARMA models are strongly consistent and asymptotically normal. It extends Thm 3.1 of Basawa and Lund (2001) on least squares estimation of PARMA models with independent errors. It is seen that the asymptotic covariance matrix of the WLS estimators obtained under dependent errors is generally different from that obtained with independent errors. The impact can be dramatic on the standard inference methods based on independent errors when the latter are dependent. Examples and simulation results illustrate the practical relevance of our findings. An application to financial data is also presented.

Number of Pages in PDF File: 25

Keywords: Weak periodic autoregressive moving average models, seasonality, weighted least squares, asymptotic normality, strong consistency, weak periodic white noise, strong mixing, primary 62M10, secondary 62M15

Accepted Paper Series