Weak Convergence to Stochastic Integrals for Econometric Applications

Hanying Liang, Peter Phillips, Hanchao Wang and Qiying Wang ()
Additional contact information
Hanying Liang: Tongji University
Hanchao Wang: Zhejiang University

No 1971, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications in econometrics involve a cointegration framework where endogeneity and nonlinearity play a major role and lead to complications in 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 asymptotic development and we provide limit results for such covariances when linear process, long memory, and mixing variates are involved in the innovations. The limit results extend earlier findings in the literature, are relevant in many econometric applications, and involve simple conditions that facilitate implementation in practice. A nonlinear extension of FM regression is used to illustrate practical application of the methods.

Keywords: Decomposition; FM regression; Linear process; Long memory; Stochastic integral; Semimartingale; alpha-mixing (search for similar items in EconPapers)
JEL-codes: C22 C65 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2014-12
New Economics Papers: this item is included in nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Econometric Theory (December 2016)

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Related works:
Journal Article: WEAK CONVERGENCE TO STOCHASTIC INTEGRALS FOR ECONOMETRIC APPLICATIONS (2016)
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