WEAK CONVERGENCE TO STOCHASTIC INTEGRALS FOR ECONOMETRIC APPLICATIONS. (24th July 2015)

• Record Type: Journal Article
• Authors: Liang, Hanying; Phillips, Peter C.B.; Wang, Hanchao; Wang, Qiying
• Is Part Of: Econometric theory. Volume 32:Number 6(2016:Dec.)
• Page Start: 1349
• Page End: 1375
• Publication Date: 2015-07-24
• Subjects: Econometrics -- Periodicals; 330.01519505
• DOI: 10.1017/S0266466615000274
• Languages: English
• ISSNs: 0266-4666

Abstract

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.