Residual-based Rank Specification Tests for AR-GARCH type models
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 distribution of 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.
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- Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
- Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- K Abadir & W Distaso, .
"Testing joint hypotheses when one of the alternatives is one-sided,"
05/13, Department of Economics, University of York.
- Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
- Horv th, Lajos & Kokoszka, Piotr, 2001. "LARGE SAMPLE DISTRIBUTION OF WEIGHTED SUMS OF ARCH(p) SQUARED RESIDUAL CORRELATIONS," Econometric Theory, Cambridge University Press, vol. 17(02), pages 283-295, April.
- Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
- Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
- Engle, Robert F & Ng, Victor K, 1993.
" Measuring and Testing the Impact of News on Volatility,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1749-78, December.
- Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
- Y. K. Tse, 2002. "Residual-based diagnostics for conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 358-374, 06.
- Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
- Wright, Jonathan H, 2000.
"Alternative Variance-Ratio Tests Using Ranks and Signs,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 18(1), pages 1-9, January.
- Tom Doan, . "RATS programs to replicate Wright's Alternative Variance Ratio test results," Statistical Software Components RTZ00168, Boston College Department of Economics.
- Oliver Linton, 1993.
"Adaptive Estimation in ARCH Models,"
Cowles Foundation Discussion Papers
1054, Cowles Foundation for Research in Economics, Yale University.
- Hansen, Bruce E, 1994.
"Autoregressive Conditional Density Estimation,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Robin L. Lumsdaine & Serena Ng, 1998.
"Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean,"
Boston College Working Papers in Economics
370, Boston College Department of Economics.
- Lumsdaine, Robin L. & Ng, Serena, 1999. "Testing for ARCH in the presence of a possibly misspecified conditional mean," Journal of Econometrics, Elsevier, vol. 93(2), pages 257-279, December.
- BAUWENS, Luc & LAURENT, SÃ©bastien & ROMBOUTS, Jeroen, 2003.
"Multivariate GARCH models: a survey,"
CORE Discussion Papers
2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hallin, M. & Werker, B.J.M., 2003.
"Semiparametric efficiency, distribution-freeness and invariance,"
Other publications TiSEM
fe20db00-786a-4261-9999-6, Tilburg University, School of Economics and Management.
- Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
- Honore, Bo E & Hu, Luojia, 2004. "On the Performance of Some Robust Instrumental Variables Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 30-39, January.
- Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
- Drost, F.C. & Werker, B.J.M., 2001.
"Semiparametric Duration Models,"
2001-11, Tilburg University, Center for Economic Research.
- Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012.
"Testing conditional asymmetry: A residual-based approach,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 36(8), pages 1229-1247.
- Philippe Lambert & Sébastien Laurent & David Veredas, 2012. "Testing conditional asymmetry. A residual based approach," ULB Institutional Repository 2013/136195, ULB -- Universite Libre de Bruxelles.
- Ploberger, Werner, 2004. "A complete class of tests when the likelihood is locally asymptotically quadratic," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 67-94.
- Drost, F.C. & Werker, B.J.M., 2004. "Semiparametric duration models," Other publications TiSEM a1895e3e-f720-454b-9613-f, Tilburg University, School of Economics and Management.
- Ploberger, Werner & Phillips, Peter C.B., 2012.
"Optimal estimation under nonstandard conditions,"
Journal of Econometrics,
Elsevier, vol. 169(2), pages 258-265.
- Halunga, Andreea G. & Orme, Chris D., 2009.
"First-Order Asymptotic Theory For Parametric Misspecification Tests Of Garch Models,"
Cambridge University Press, vol. 25(02), pages 364-410, April.
- Andreea Halunga & Chris D. Orme, 2007. "First order asymptotic theory for parametric misspecification tests of GARCH models," The School of Economics Discussion Paper Series 0721, Economics, The University of Manchester.
- Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Other publications TiSEM aa253902-af93-4e1e-b974-2, Tilburg University, School of Economics and Management.
- Berkes, Istv n & Horv th, Lajos & Kokoszka, Piotr, 2003. "Asymptotics For Garch Squared Residual Correlations," Econometric Theory, Cambridge University Press, vol. 19(04), pages 515-540, August.
- Sun, Yiguo & Stengos, Thanasis, 2006. "Semiparametric efficient adaptive estimation of asymmetric GARCH models," Journal of Econometrics, Elsevier, vol. 133(1), pages 373-386, July.
- Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January.
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