The Annual Meeting of the Finnish Statistical Society, Vaasa, 17-18 May 2001
Evaluating GARCH models
Timo Teräsvirta, Stockholm School of Economics
Abstract: When a statistical model has been estimated it should be evaluated. In this lecture a unified framework for testing the adequacy of an estimated GARCH model is presented. Parametric LM or LM type tests of no ARCH in standardized errors, linearity, and parameter constancy are proposed and discussed. The asymptotic null distributions of the tests are standard, which makes application easy. Versions of the tests that are robust against nonnormal errors are provided. The finite sample properties of the test statistics are investigated by simulation. Not surprisingly, the robust tests prove superior to the nonrobust ones when the errors are nonnormal. Our tests also compare favourably in terms of power with misspecification tests previously proposed in the literature.
In the second part of the lecture, ways of comparing GARCH and exponential GARCH models are discussed. Three nonnested tests for testing these two models against each other are presented and their finite sample properties considered by simulation. Finally, an application of these techniques to the thirty most actively traded stocks at the Stockholm Stock Exchange is discussed.
The first part of the lecture is based on a working paper by S. Lundbergh and Timo Teräsvirta: "Evaluating GARCH models". The paper is downloadable at www.hhs.se/stat/research/nonlinear.htm.