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CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: LP -APPROXIMABILITY VERSUS BROWNIAN MOTION

Published online by Cambridge University Press:  01 June 2009

Kairat T. Mynbaev
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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.

Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 748 - 763
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The paper has been significantly improved following comments and suggestions by three anonymous referees and an associate editor. I am especially grateful to one of the referees for a cryptic remark that my paper “opens the way to use the important results of Cremers and Kadelka (1986).”

References

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