Residual-based rank specification tests for AR-GARCH type models

E. Andreou, B.J.M. Werker

Research output: Contribution to journalArticleScientificpeer-review

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. We also apply our method to backtesting Value-at-Risk. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR–GARCH residuals obtained through Gaussian quasi maximum likelihood estimation. To be precise, we give exact expressions for the limiting null distribution of the test statistics applied to (standardized) residuals, and find that standard critical values often, though not always, lead to conservative tests. For this result, we give simple necessary and 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. An empirical application illustrates the relevance of these tests to the AR–GARCH models for weekly stock market return indices of some major and emerging countries.
Original languageEnglish
Pages (from-to)305-331
JournalJournal of Econometrics
Volume185
Issue number2
DOIs
Publication statusPublished - Apr 2015

Fingerprint

Generalized autoregressive conditional heteroscedasticity
Specification test
Test statistic
Asymptotic distribution
Approximation
Limiting distribution
Backtesting
Serials
Stock market returns
Simulation
Symmetry
Emerging countries
Autocorrelation
Critical value
Value at risk
Quasi-maximum likelihood estimation
Structural breaks

Keywords

  • conditional heteroscedasticity
  • linear and quadratic residual autocorrelation tests
  • model misspecification test
  • nonlinear time series
  • parameter constancy
  • residual symmetry tests

Cite this

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title = "Residual-based rank specification tests for AR-GARCH type models",
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. We also apply our method to backtesting Value-at-Risk. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR–GARCH residuals obtained through Gaussian quasi maximum likelihood estimation. To be precise, we give exact expressions for the limiting null distribution of the test statistics applied to (standardized) residuals, and find that standard critical values often, though not always, lead to conservative tests. For this result, we give simple necessary and 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. An empirical application illustrates the relevance of these tests to the AR–GARCH models for weekly stock market return indices of some major and emerging countries.",
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Residual-based rank specification tests for AR-GARCH type models. / Andreou, E.; Werker, B.J.M.

In: Journal of Econometrics, Vol. 185, No. 2, 04.2015, p. 305-331.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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. We also apply our method to backtesting Value-at-Risk. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR–GARCH residuals obtained through Gaussian quasi maximum likelihood estimation. To be precise, we give exact expressions for the limiting null distribution of the test statistics applied to (standardized) residuals, and find that standard critical values often, though not always, lead to conservative tests. For this result, we give simple necessary and 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. An empirical application illustrates the relevance of these tests to the AR–GARCH models for weekly stock market return indices of some major and emerging countries.

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