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Almost Sure Bounds On The Estimation Error For Ols Estimators When The Regressors Include Certain Mfi(1) Processes

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  • Bauer, Dietmar

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.

Suggested Citation

  • Bauer, Dietmar, 2009. "Almost Sure Bounds On The Estimation Error For Ols Estimators When The Regressors Include Certain Mfi(1) Processes," Econometric Theory, Cambridge University Press, vol. 25(2), pages 571-582, April.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:02:p:571-582_09
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    Cited by:

    1. B. Nielsen, 2009. "Test for cointegration rank in general vector autoregressions," Economics Papers 2009-W10, Economics Group, Nuffield College, University of Oxford.
    2. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, vol. 3(1), pages 1-31, March.
    3. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 156, March.

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