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2014 | OriginalPaper | Chapter

7. Nonparametric Distribution-Free Model Checks for Multivariate Dynamic Regressions

Authors : Miguel A. Delgado, J. Carlos Escanciano

Published in: Contemporary Developments in Statistical Theory

Publisher: Springer International Publishing

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Abstract

This article proposes asymptotic distribution-free speci.cation tests for parametric regres-sion models under time series processes with higher conditional moments of unknown form and multivariate regressors. The proposed test statistics are continuous functionals of a Khmaladze-Rossenblatt.s transform of a function-parametric residual marked process. Thus, our results extend those of Koul and Stute (1999) and Khmaladze and Koul (2004) to the multivariate time-series heteroskedastic case. The asymptotic theory is formally established using new weak convergence theorems for function-parametric processes. Finally, we compare the power prop-erties of bootstrap-based tests and our martingale-transform-based Cramér-von Mises test by a limited Monte Carlo experiment. We conclude that our new test compares very well to bootstrap tests for the alternatives considered and that the asymptotic results are good approximations for .nite sample distributions.

_AMS 2000 subject classi.cation. 62M07, 62G09, 62G10.

Key words and phrases. Function-parametric empirical processes, Khmaladze.s transformation, Rosenblatt.s trans-formation, Omnibus tests.

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The martingale trasform has also been variously referred to as: an innovation approach (Khmaladze, 1988), and an innovation process approach (Stute, Thies, and Zhu, 1998).

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Title: Nonparametric Distribution-Free Model Checks for Multivariate Dynamic Regressions
Authors: Miguel A. Delgado
J. Carlos Escanciano
Publisher: Springer International Publishing
Book: Contemporary Developments in Statistical Theory
Print ISBN: 978-3-319-02650-3

Electronic ISBN: 978-3-319-02651-0

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-02651-0_7

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