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The GLS Transformation Matrix and a Semi-recursive Estimator for the Linear Regression Model with ARMA Errors

Published online by Cambridge University Press:  18 October 2010

John W. Galbraith  and
Victoria Zinde-Walsh
John W. Galbraith
Affiliation:
McGill University
Victoria Zinde-Walsh
Affiliation:
McGill University
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Abstract

For a general stationary ARMA(p,q) process u we derive the exact form of the orthogonalizing matrix R such that R′R = Σ−1, where Σ = E(uu′) is the covariance matrix of u, generalizing the known formulae for AR(p) processes. In a linear regression model with an ARMA(p,q) error process, transforming the data by R yields a regression model with white-noise errors. We also consider an application to semi-recursive (being recursive for the model parameters, but not for the parameters of the error process) estimation.

Type
Articles
Information
Econometric Theory , Volume 8 , Issue 1 , March 1992 , pp. 95 - 111
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

1.Amemiya, T.Advanced Econometrics. Cambridge: Harvard University Press, 1985.Google Scholar
2.Box, G.E.P. & Jenkins, G.M.. Time Series Analysis Forecasting and Control. San Francisco: Holden-Day, 1970.Google Scholar
3.Brown, R.L., Durbin, J. & Evans, J.M.. Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Soceity B (1975): 149–192.Google Scholar
4.Dufour, J.-M.Recursive stability analysis of linear regression relationships. Journal of Econometrics 19 (1982): 31–76.Google Scholar
5.Franke, J.A Levinson-Durbin recursion for autoregressive-moving average processes. Biometrika 72 (1985): 573–581.CrossRefGoogle Scholar
6.Hannan, E. J. & Deistler, M.. The Statistical Theory of Linear Systems. New York: Wiley, 1988.Google Scholar
7.Hannan, E.J. & Kavalieris, L.. A method for autoregressive-moving average estimation. Biometrika 72 (1984): 273–280.Google Scholar
8.Hannan, E.J., Kavalieris, L. & Mackisack, M.. Recursive estimation of linear systems. Biometrika 73 (1986): 119–133.CrossRefGoogle Scholar
9.Hannan, E.J. & McDougall, A.J.. Regression procedures for ARMA estimation. Journal of the American Statistical Association 83 (1988): 490–498.Google Scholar
10.Hannan, E.J. & Rissanen, J.. Recursive estimation of mixed autoregressive-moving average order. Biometrika 69 (1982): 81–94.Google Scholar
11.Harvey, A.C.The Econometric Analysis of Time Series. Oxford: Philip Allan, 1981.Google Scholar
12.Harvey, A.C. & Phillips, G.D.A.. Maximum likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika 66 (1979): 49–58.Google Scholar
13.Hendry, D.F.PC-GIVE: An Interactive Econometric Modelling System. Oxford: Institute of Economics and Statistics, 1989.Google Scholar
14.Hendry, D.F. & Neale, A.J.. The Impact of Structural Breaks on Unit-Root Tests. Mimeo., Nuffield College, Oxford, 1989.Google Scholar
15.Judge, G.G., Hill, R.C., Griffiths, W.E., Lutkepohl, H. & Lee, T.C.. The Theory and Practice of Econometrics, 2nd ed. New York: Wiley, 1985.Google Scholar
16.Ljung, L. & Soderstrom, T.. Theory and Practice of Recursive Identification. Cambridge: MIT Press, 1983.Google Scholar
17.Ploberger, W., Kontrus, K. & Kramer, W.. A new test for structural stability in linear regression. Journal of Econometrics 40 (1989); 307–318.CrossRefGoogle Scholar
18.Said, S.E. & Dickey, D.A.. Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71 (1984): 599–607.Google Scholar
19.Spanos, A.Statistical Foundations of Econometric Modelling. Cambridge: Cambridge University Press, 1986.Google Scholar
20.Zinde-Walsh, V.Some exact formulae for autoregressive-moving average processes. Econometric Theory 4 (1988): 384–402. Errata, Econometric Theory 6 (1990): 293.Google Scholar
21.Zinde-Walsh, V. & Galbraith, J.W.. Estimation of a linear regression model with stationary ARMA(p,q) errors. Journal of Econometrics 47 (1991): 333–357.CrossRefGoogle Scholar