Publication Type

Journal Article

Publication Date

12-2016

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.

Keywords

Decomposition, FM regression, Linear process, Long memory, Stochastic integral, Semimartingale, α−mixing

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometric Theory

Volume

32

Issue

6

First Page

1349

Last Page

1375

ISSN

0266-4666

Identifier

10.1017/S0266466615000274

Publisher

Cambridge University Press (CUP): HSS Journals

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://doi.org/10.1017/S0266466615000274

Included in

Econometrics Commons

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