Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models

• M. Dolores Jiménez-Gamero ^[3] ; Sangyeol Lee ^[1] ; Simos G. Meintanis ^[2]
  1. [1] Seoul National University

     Seoul National University

     Corea del Sur

     
  2. [2] National and Kapodistrian University of Athens

     National and Kapodistrian University of Athens

     Dimos Athens, Grecia

     
  3. [3] Department of Statistics and Operations Research, University of Sevilla, Sevilla, Spain

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 3, 2020, págs. 682-703
• Idioma: inglés
• DOI: 10.1007/s11749-019-00676-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider a goodness-of-fit test for certain parametrizations of conditionally heteroscedastic time series with unobserved components. Our test is quite general in that it can be employed to validate any given specification of arbitrary order and may even be invoked for testing not just GARCH models but also some related models such as autoregressive conditional duration models. The test statistic utilizes the characterization of Bierens (J Econom 20:105–134, 1982) and may be written down in a convenient closed-form expression. Consistency of the test is proved, and the asymptotic distribution of the test statistic under the null hypothesis is studied. Since this distribution depends on unknown quantities, two bootstrap resampling schemes are investigated and compared in order to approximate critical points and actually carry out the test. Finite-sample results are presented as well as applications of the proposed procedures to real data from the financial markets.

• Referencias bibliográficas
  • Bauwens L, Giot P (2003) Asymmetric ACD models: introducing price information in ACD models. Empir Econ 28:709–731
  • Berkes I, Horváth L, Kokoszka PS (2003a) Asymptotics for garch squared residual correlations. Econom Theor 19:515–540
  • Berkes I, Horváth L, Kokoszka PS (2003b) GARCH processes: structure and estimation. Bernoulli 9:201–227
  • Bierens HJ (1982) Consistent model specification tests. J Econom 20:105–134
  • Davis RA, Matsui M, Mikosch T, Wan P (2018) Applications of distance correlation to time series. Bernoulli 24:3087–3116
  • Dufour A, Engle R (2000) Time and the price impact of a trade. J Finance 55:2467–2498
  • Engle R, Russell J (1998) Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica 66:1127–1162
  • Escanciano JC (2008) Joint and marginal specification tests for conditional mean and variance models. J Econom 143:74–87
  • Fernandes M, Gramming J (2005) Nonparametric specification tests for conditional duration models. J Econom 127:16–38
  • Fokianos K, Pitsillou M (2018) Testing independence for multivariate time series via the auto-distance correlation matrix. Biometrika 105:337–352
  • Francq C, Zakoïan JM (2004) Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes. Bernoulli 10:605–637
  • Francq C, Zakoïan JM (2010) GARCH models: structure, statistical inference and financial applications. Wiley, New York
  • Francq C, Winterberger O, Zakoïan JM (2013) GARCH model without positivity constraints: exponential or log GARCH? J Econom 177:34–46
  • Francq C, Winterberger O, Zakoïan JM (2018) Goodness-of-fit tests for Log-GARCH and EGARCH models. Test 27:27–51
  • Ghoudi K, Rémillard B (2014) Comparison of specification tests for GARCH models. Comput Stat Data Anal 76:291–300
  • Ghoudi K, Rémillard B (2018) Serial independence tests for innovations of conditional mean and variance models. Test 27:3–26
  • González-Manteiga W, Zubelli JP, Monsalve-Cobis A, Febrero-Bande M (2017) Goodness-of-fit test for stochastic volatility models. In: Ferger...
  • Halunga AG, Orme CD (2009) First-order asymptotic theory for parametric misspecification tests of GARCH models. Econom Theor 25:364–410
  • Hlávka Z, Hušková M, Kirch C, Meintanis SG (2017) Fourier-type tests involving martingale difference processes. Econom Rev 36:468–492
  • Hong Y (1999) Hypothesis testing in time series via the empirical characteristic function: a generalized spectral density approach. J Am Stat...
  • Hong Y, Lee TH (2003) Diagnostic checking for the adeciacy of nonlinear time series models. Econom Theor 19:1065–1121
  • Jeong M (2017) Residual-based GARCH bootstrap and second order asymptotic refinement. Econom Theor 33:779–790
  • Jiménez-Gamero MD, Pardo-Fernández JC (2017) Empirical characteristic function tests for GARCH innovation distribution using multipliers....
  • Jondeau E, Poon SH, Rockinger M (2007) Financial modeling under non-Gaussian distributions. Springer, London
  • Leucht A, Kreiss JP, Neumann MH (2015) A model specification test for GARCH(1,1) processes. Scand J Stat 42:1167–1193
  • Meintanis SG, Milošević B, Obradović M (2018) Goodness-of-fit tests in conditional duration models. Stat Pap. https://doi.org/10.1007/s00362-017-0930-8
  • Monsalve-Cobis A, González-Manteiga W, Febrero-Bande M (2011) Goodness-of-fit test for interest rate models: an approach based on empirical...
  • Nolan JP (2013) Multivariate elliptically contoured stable distribution: theory and estimation. Comput Stat 28:2067–2089
  • R Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/....
  • Rachev S, Mittnik S (2000) Stable Paretian models in finance. Wiley, New York
  • Stinchcombe MB, White H (1998) Consistent specification testing with nuisance parameters present only under the alternative. Econom Theor...
  • Székely GJ, Rizzo ML, Bakirov NK (2007) Measuring and testing dependence by correlation of distances. Ann Stat 35:1769–2794
  • eräsvirta T (2009) An introduction to univariate GARCH models. In: Andersen TG et al (eds) Handbook of financial time series. Springer, Berlin,...
  • Zheng Y, Li WK, Li G (2018) A robust goodness-of-fit test for generalized autoregressive conditionally heteroscedastic models. Biometrika...