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On a distributional bound arising in autoregressive model fitting

Part of: Stochastic processes Inference from stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

F. Papangelou
F. Papangelou*
Affiliation:
University of Manchester
*
∗ Postal address: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK.
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Abstract

In the theory of autoregressive model fitting it is of interest to know the asymptotic behaviour, for large sample size, of the coefficients fitted. A significant role is played in this connection by the moments of the norms of the inverse sample covariance matrices. We establish uniform boundedness results for these, first under generally weak conditions and then for the special case of (infinite order) processes. These in turn imply corresponding ergodic theorems for the matrices in question.

Keywords

ASYMPTOTICS OF COEFFICIENT ESTIMATORS AND INVERSE SAMPLE COVARIANCE MATRICES

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60F25: $L^p$-limit theorems 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 401 - 408
Copyright
Copyright © Applied Probability Trust 1994 

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References

[1] Bhansali, R. J. and Papangelou, F. (1991) Convergence of moments of least squares estimators for the coefficients of an autoregressive process of unknown order. Ann. Statist. 19, 1155–1162.CrossRefGoogle Scholar
[2] Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods , 2nd edn. Springer-Verlag, New York.CrossRefGoogle Scholar