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Nonparametric Bootstrap Tests for Independence of Generalized Errors

Center for Applied Economic & Policy Research Working Paper No. 023-2009

36 Pages Posted: 18 Dec 2009 Last revised: 16 Jan 2015

Zaichao Du

Southwestern University of Finance and Economics (SWUFE) - Research Institute of Economics & Management; Indiana University Bloomington - Department of Economics

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Date Written: January 15, 2015

Abstract

In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable transformation are independent and identically distributed. The latter is a key identification assumption in many nonlinear economic models. Our tests are based on a classical sample dependence measure, the Hoeffding-Blum-Kiefer-Rosenblat-type empirical process applied to generalized residuals. We establish a uniform expansion of the process, thereby deriving an explicit expression for the parameter estimation effect, which causes our tests not to be nuisance parameter-free. To circumvent this problem, we propose a multiplier-type bootstrap to approximate the limit distribution. Our bootstrap procedure is computationally very simple as it does not require a reestimation of the parameters in each bootstrap replication. In a simulation study, we apply our method to test the adequacy of ARMA-GARCH and Hansen (1994) skewed t models, and document a good finite sample performance of our test. Finally, an empirical application to daily exchange rate data highlights the merits of our approach.

Keywords: Independence; Generalized errors; Goodness-of-Fit; Identification; Empirical process; Parameter estimation uncertainty; Bootstrap; GARCH; Skewed t distribution

JEL Classification: C12, C14, C52

Suggested Citation

Du, Zaichao, Nonparametric Bootstrap Tests for Independence of Generalized Errors (January 15, 2015). Center for Applied Economic & Policy Research Working Paper No. 023-2009. Available at SSRN: https://ssrn.com/abstract=1524850 or http://dx.doi.org/10.2139/ssrn.1524850

Zaichao Du (Contact Author)

Southwestern University of Finance and Economics (SWUFE) - Research Institute of Economics & Management ( email )

55 Guanghuacun Street
Chengdu, Sichuan 610074
China

Indiana University Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

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