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ALMOST SURE BOUNDS ON THE ESTIMATION ERROR FOR OLS ESTIMATORS WHEN THE REGRESSORS INCLUDE CERTAIN MFI(1) PROCESSES

Published online by Cambridge University Press:  01 April 2009

Dietmar Bauer
Dietmar Bauer*
Affiliation:
arsenal research
*
*Address correspondence to Dietmar Bauer, arsenal research, Business Field HCMT, Giefingg. 2, A-1210 Wein; e-mail: Dietmar.Bauer@arsenal.ac.at.
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Abstract

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Lai and Wei (1983, Annals of Statistics 10, 154–166) state in their Theorem 1 that the estimators of the regression coefficients in the regression $y_t = x_t^, t ∈ ℕ are almost surely (a.s.) consistent under the assumption that the minimum eigenvalue λmin(T) of $\sum\nolimits_{t = 1}^T {x_t } x'_t $ tends to infinity (a.s.) and log(λmax(T))/λmin(T) → 0 (a.s.) where λmax(T) denotes the maximal eigenvalue. Moreover the rate of convergence in this case equals $O(\root \of {\log (\lambda _{max} (T))/\lambda _{min} (T)})$. In this note xt is taken to be a particular multivariate multifrequency I(1) processes, and almost sure rates of convergence for least squares estimators are established.

Information

Type
Notes and Problems
Information
Econometric Theory , Volume 25 , Issue 2 , April 2009, pp. 571 - 582
Copyright
Copyright © Cambridge University Press 2009

References

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