Working Paper: CEPR ID: DP9583
Authors: Elena Andreou; Bas J. M. Werker
Abstract: This paper derives the asymptotic distribution for a number of rank-based and classical residual specification tests in AR-GARCH type models. We consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation, residual symmetry, and no structural breaks. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR-GARCH type residuals obtained through QMLE estimation. To be precise, we give exact expressions for the limiting null distributionof the test statistics applied to residuals, and find that standard critical values often lead to conservative tests. For this result, we give simple sufficient conditions. Simulations show that our asymptotic approximations work well for a large number of AR-GARCH models and parameter values. We also show that the rank-based tests often, though not always, have superior power properties over the classical tests, even if they are conservative. We thereby provide a useful extension to the econometrician's toolkit. An empirical application illustrates the relevance of these tests to the AR-GARCH models for the weekly stock market return indices of some major and emerging countries.
Keywords: conditional heteroskedasticity; linear and quadratic residual autocorrelation tests; model misspecification test; nonlinear time series; parameter constancy; residual symmetry tests
JEL Codes: C22; C32; C51; C52
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| asymptotic distribution of the tests does not require size correction (C46) | tests remain valid (C52) |
| rank-based tests exhibit superior power properties (C52) | classical tests (C12) |
| tests are robust to different innovation distributions (C46) | handle estimation uncertainty (C51) |
| rank-based tests handle estimation uncertainty (C51) | performance of the tests (C52) |