Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models
AbstractThe 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 Theorem 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.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Journal of Time Series Analysis.
Volume (Year): 32 (2011)
Issue (Month): 6 (November)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
Other versions of this item:
- Francq, Christian & Roy, Roch & Saidi, Abdessamad, 2011. "Asymptotic properties of weighted least squares estimation in weak parma models," MPRA Paper 28721, University Library of Munich, Germany.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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