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WEAK CONVERGENCE TO STOCHASTIC INTEGRALS FOR ECONOMETRIC APPLICATIONS

Published online by Cambridge University Press:  24 July 2015

Hanying Liang ,
Peter C.B. Phillips ,
Hanchao Wang  and
Qiying Wang
Hanying Liang
Affiliation:
Tongji University
Peter C.B. Phillips
Affiliation:
Yale University
Hanchao Wang
Affiliation:
Zhejiang University
Qiying Wang*
Affiliation:
The University of Sydney
*
*Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: qiying@maths.usyd.edu.au.
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Abstract

Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on functional weak convergence. In establishing such convergence, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications involve a cointegration framework where endogeneity and nonlinearity play major roles and complicate the limit theory. This paper explores weak convergence limit theory to stochastic integral functionals in such settings. We use a novel decomposition of sample covariances of functions of I (1) and I (0) time series that simplifies the asymptotics and our limit results for such covariances hold for linear process, long memory, and mixing variates in the innovations. These results extend earlier findings in the literature, are relevant in many applications, and involve simple conditions that facilitate practical implementation. A nonlinear extension of FM regression is used to illustrate practical application of the methods.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 6 , December 2016 , pp. 1349 - 1375
Copyright
Copyright © Cambridge University Press 2015 

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