Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models
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 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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Volume (Year): 32 (2011)
Issue (Month): 6 (November)
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- Christian Francq & Jean-Michel Zakoïan, 2009.
"Bartlett's formula for a general class of nonlinear processes,"
Journal of Time Series Analysis,
Wiley Blackwell, vol. 30(4), pages 449-465, 07.
- Francq, Christian & Zakoian, Jean-Michel, 2009. "Bartlett's formula for a general class of non linear processes," MPRA Paper 13224, University Library of Munich, Germany.
- Peiro, Amado, 1994. "Daily seasonality in stock returns : Further international evidence," Economics Letters, Elsevier, vol. 45(2), pages 227-232, June.
- Shiqing Ling & Michael McAleer, 2001.
"Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models,"
ISER Discussion Paper
0534, Institute of Social and Economic Research, Osaka University.
- Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
- Christian Francq & Jean-Michel Zakoïan, 1997.
"Estimating Weak Garch Representations,"
97-40, Centre de Recherche en Economie et Statistique.
- Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-127, January.
- QIN SHAO & ROBERT Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, 05.
- Abdelhakim Aknouche & Abdelouahab Bibi, 2009. "Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 19-46, 01.
- Christian Francq & Jean-Michel Zakoïan, 2008. "Barlett’s Formula for Non Linear Processes," Working Papers 2008-05, Centre de Recherche en Economie et Statistique.
- Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
- Philip Hans Franses & Richard Paap, 2000. "Modelling day-of-the-week seasonality in the S&P 500 index," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 483-488.
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