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STRONG CONSISTENCY RESULTS FOR LEAST SQUARES ESTIMATORS IN GENERAL VECTOR AUTOREGRESSIONS WITH DETERMINISTIC TERMS

Published online by Cambridge University Press:  22 April 2005

Bent Nielsen
Bent Nielsen
Affiliation:
University of Oxford
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Abstract

A vector autoregression with deterministic terms and with no restrictions to its characteristic roots is considered. Strong consistency results for the least squares statistics are presented. This extends earlier results where deterministic terms have not been considered. In addition the convergence rates are improved compared with earlier results.Comments from S. Johansen are gratefully acknowledged.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 3 , June 2005 , pp. 534 - 561
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Anderson, T.W. (1959) On asymptotic distributions of estimates of parameters of stochastic difference equations. Annals of Mathematical Statistics 30, 676–687.Google Scholar
Chan, N.H. & C.Z. Wei (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367–401.Google Scholar
Duflo, M., R. Senoussi, & R. Touati (1991) Propriétés asymptotiques presque sûre de l'estimateur des moindres carrés d'un modèle autorégressif vectoriel. Annales de l'Institut Henri Poincaré—Probabilités et Statistiques 27, 1–25.Google Scholar
Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation. Econometrica 50, 987–1008.Google Scholar
Fuller, W.A., D.P. Hasza, & J.J. Goebel (1981) Estimation of the parameters of stochastic difference equations. Annals of Statistics 9, 531–543.Google Scholar
Gantmacher, F.R. (2000) The Theory of Matrices, vol 1. Reprint. Chelsea Publishing.
Gradshteyn, I.S. & I.M. Ryzhik (1965) Table of Integrals, Series and Products. Academic Press.
Hall, P. & C.C. Heyde (1980) Martingale Limit Theory and Its Applications. Academic Press.
Herstein, I.N. (1975) Topics in Algebra, 2nd ed. Wiley.
Jeganathan, P. (1988) On the strong approximation of the distributions of estimators in linear stochastic models, parts I and II: Stationary and explosive AR models. Annals of Statistics 16, 1283–1314.Google Scholar
Johansen, S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.
Johansen, S. (2000) A Bartlett correction factor for tests on the cointegrating relations. Econometric Theory 16, 740–778.Google Scholar
Lai, T.L. & C.Z. Wei (1982) Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Annals of Statistics 10, 154–166.Google Scholar
Lai, T.L. & C.Z. Wei (1983a) A note on martingale difference sequences satisfying the local Marcinkiewicz-Zygmund condition. Bulletin of the Institute of Mathematics, Academia Sinica 11, 1–13.Google Scholar
Lai, T.L. & C.Z. Wei (1983b) Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters. Journal of Multivariate Analysis 13, 1–23.Google Scholar
Lai, T.L. & C.Z. Wei (1985) Asymptotic properties of multivariate weighted sums with applications to stochastic regression in linear dynamic systems. In P.R. Krishnaiah (ed.), Multivariate Analysis, vol. VI, pp. 375–393. Elsevier Science Publishers.
Nielsen, B. (2000) The Asymptotic Distribution of Likelihood Ratio Test Statistics for Cointegration in Unstable Vector Autoregressive Processes. Discussion paper, Nuffield College, Oxford.
Nielsen, B. (2001a) The asymptotic distribution of unit root tests of unstable autoregressive processes. Econometrica 69, 211–219.Google Scholar
Nielsen, B. (2001b) Weak Consistency of Criterions for Order Determination in a General Vector Autoregression. Discussion paper, Nuffield College, Oxford.
Phillips, P.C.B. (1991) Optimal inference in cointegrated systems. Econometrica 59, 283–306.Google Scholar
Pötscher, B.M. (1989) Model selection under nonstationarity: Autoregressive models and stochastic linear regression models. Annals of Statistics 17, 1257–1274.Google Scholar
Rubin, H. (1950) Consistency of maximum-likelihood estimates in the explosive case. In T.C. Koopmans (ed.), Statistical Inference in Dynamic Economic Models, pp. 356–364. Wiley.
Wei, C.Z. (1992) On predictive least squares principles. Annals of Statistics 20, 1–42.Google Scholar
Wei, C.Z. (1985) Asymptotic properties of least-squares estimates in stochastic regression models. Annals of Statistics 13, 1498–1508.Google Scholar