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Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion

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  • Mynbaev, Kairat T.

Abstract

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

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  • Mynbaev, Kairat T., 2009. "Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion," Econometric Theory, Cambridge University Press, vol. 25(3), pages 748-763, June.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:03:p:748-763_09
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    Cited by:

    1. Kairat T. Mynbaev, 2011. "Regressions with asymptotically collinear regressors," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 304-320, July.
    2. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2017. "Weak convergence of linear and quadratic forms and related statements on Lp-approximability," MPRA Paper 101686, University Library of Munich, Germany, revised Dec 2018.
    3. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.
    4. Uematsu, Yoshimasa, 2016. "Asymptotic efficiency of the OLS estimator with singular limiting sample moment matrices," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 104-110.
    5. Mynbayev, Kairat, 2007. "OLS Asymptotics for Vector Autoregressions with Deterministic Regressors," MPRA Paper 101688, University Library of Munich, Germany, revised 2018.
    6. Yoshimasa Uematsu, 2011. "Regression with a Slowly Varying Regressor in the Presence of a Unit Root," Global COE Hi-Stat Discussion Paper Series gd11-209, Institute of Economic Research, Hitotsubashi University.
    7. Yoshimasa Uematsu, 2011. "Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices," Global COE Hi-Stat Discussion Paper Series gd11-208, Institute of Economic Research, Hitotsubashi University.

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