A Joint Portmanteau Test for Conditional Mean and Variance Time‐Series Models

22 Pages Posted: 30 Dec 2014

See all articles by Carlos Velasco

Carlos Velasco

Universidad Carlos III de Madrid - Department of Economics

Xuexin Wang

Xiamen University

Date Written: January 2015

Abstract

In this article, we propose a new joint portmanteau test for checking the specification of parametric conditional mean and variance functions of linear and nonlinear time‐series models. The use of a joint test is motivated for complete control of the asymptotic size since marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified. The new test is based on an asymptotically distribution‐free transformation on the sample autocorrelations of both normalized residuals and squared normalized residuals. This makes it unnecessary to full detail the asymptotic properties of the estimates used to obtain residuals, which could be inefficient two‐step ones, avoiding also choices of maximum lag parameters increasing with sample length to control asymptotic size. The robust versions of the new test also properly account for higher‐order moment dependence at a reduced cost. The finite‐sample performance of the new test is compared with that of well‐known tests through simulations.

Keywords: Model diagnostic checking, portmanteau statistic, estimation effect, GARCH model specification testing, residual serial correlation

Suggested Citation

Velasco, Carlos and Wang, Xuexin, A Joint Portmanteau Test for Conditional Mean and Variance Time‐Series Models (January 2015). Journal of Time Series Analysis, Vol. 36, Issue 1, pp. 39-60, 2015. Available at SSRN: https://ssrn.com/abstract=2543843 or http://dx.doi.org/10.1111/jtsa.12091

Carlos Velasco (Contact Author)

Universidad Carlos III de Madrid - Department of Economics ( email )

Calle Madrid 126
Getafe, 28903
Spain
+34-91 6249646 (Phone)
+34-91 6249875 (Fax)

Xuexin Wang

Xiamen University

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