Testing for Autocorrelation and Unit Roots in the Presence of Conditional Heteroskedasticity of Unknown Form

UC Santa Cruz Economics Working Paper No. 540

56 Pages Posted: 11 Nov 2003

See all articles by Binbin Guo

Binbin Guo

First Quadrant, L.P.

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Date Written: July 4, 2001

Abstract

The presence of conditional heteroskedasticity invalidates standard autocorrelation tests such as the Durbin-Watson statistic and its many variants, and reduces the power of standard unit root tests like the Dickey-Fuller test. This paper addresses the problem of testing for AR(1) and AR(p) alternatives in the presence of conditional heteroskedasticity, constructs new autocorrelation tests (called g- and gl- tests), and derives an asymptotic theory for the new statistics. The g test is shown to be robust to any form of conditional heteroskedasticity, while the gl test is robust to the joint presence of conditional heteroskedasticity and lagged dependent variables. The paper also develops a GLS-type unit root test that allows for conditional heteroskedasticity. Its limit distribution turns out to be a convex mixture of the Dickey-Fuller distribution and the standard normal distribution. It is shown that the GLS statistic improves the power of the Dickey-Fuller test under condictional heteroskedasticity. Some Monte Carlo simulations with the new tests are reported.

Keywords: Autoregression, Box Pierce test, conditional GLS, conditional heteroskedasticity, DW test, g-test, LM test, gl-test, serial correlation test, DF test, unit root test

JEL Classification: C22

Suggested Citation

Guo, Binbin and Phillips, Peter C. B., Testing for Autocorrelation and Unit Roots in the Presence of Conditional Heteroskedasticity of Unknown Form (July 4, 2001). UC Santa Cruz Economics Working Paper No. 540, Available at SSRN: https://ssrn.com/abstract=393641 or http://dx.doi.org/10.2139/ssrn.393641

Binbin Guo (Contact Author)

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Peter C. B. Phillips

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