Testing for Reduction to Random Walk in Autoregressive Conditional Heteroskedasticity Models

Klüppelberg, Claudia; Maller, R. A.; Van De Vyver, M. und Wee, D. (2001): Testing for Reduction to Random Walk in Autoregressive Conditional Heteroskedasticity Models. Sonderforschungsbereich 386, Discussion Paper 266

Abstract

The AR-ARCH and AR-GARCH models, which allow for conditional heteroskedasticity and autoregression, reduce to random walk or white noise for some values of the parameters. We consider generalised versions of the AR-ARCH(1) and AR-GARCH(1,1) models, and, under mild assumptions, calculate the asymptotic distributions of pseudo-likelihood ratio statistics for testing hypotheses that reect these reductions. These hypotheses are of two kinds: the conditional volatility parameters may take their boundary values of zero, or the autoregressive component may take the form of a unit root process or not in fact be present. The limiting distributions of the resulting test statistics can be expressed in terms of functionals of Brownian motion related to the Dickey-Fuller statistic, together with independent chi-square components. The finite sample performances of the test statistics are assessed by simulations, and percentiles are tabulated. The results have applications in the analysis of financial time series and random coefficient models.

• Dokumententyp: Paper
• Keywords: AR-ARCH and AR-GARCH models, conditional heteroskedasticity, autoregression, unit root, Dickey-Fuller test, pseudo-likelihood ratio test
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch