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

Dietmar Bauer ()

Econometric Theory, 2009, vol. 25, issue 2, 571-582

Abstract: 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^' \beta + \varepsilon _{\rm{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.

Date: 2009
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