Empirical characteristic function tests for GARCH innovation distribution using multipliers

References

• Bollerslev T. Generalized, autoregressive conditional heteroskedasticity. J Econometrics. 1986;31:307–327. doi: 10.1016/0304-4076(86)90063-1
   Web of Science ®Google Scholar
• Hall P, Yao Q. Inference in ARCH and GARCH models with heavy-tailed errors. Econometrica. 2003;71:285–317. doi: 10.1111/1468-0262.00396
   Web of Science ®Google Scholar
• Berkes I, Horváth L, Kokoszka P. GARCH processes: structure and estimation. Bernoulli. 2003;9:201–227. doi: 10.3150/bj/1068128975
   Web of Science ®Google Scholar
• Francq C, Zakoïan JM. Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes. Bernoulli. 2004;10:605–637. doi: 10.3150/bj/1093265632
   Web of Science ®Google Scholar
• Escanciano JC. Quasimaximum likelihood estimation of semi-strong GARCH models. Econometric Theory. 2009;25:561–570. doi: 10.1017/S0266466609090689
   Web of Science ®Google Scholar
• Klar B, Lindner F, Meintanis SG. Specification tests for the error distribution in GARCH models. Comput Statist Data Anal. 2012;56:3587–3598. doi: 10.1016/j.csda.2010.05.029
   Web of Science ®Google Scholar
• Bai J, Chen Z. Testing multivariate distributions in GARCH models. J Econometrics. 2008;143:19–36. doi: 10.1016/j.jeconom.2007.08.012
   Web of Science ®Google Scholar
• Berkes I, Horváth L. The efficiency of the estimators of the parameters in GARCH processes. Ann Statist. 2004;32:633–655. doi: 10.1214/009053604000000120
   Web of Science ®Google Scholar
• Koul HL, Ling S. Fitting an error distribution in some heteroscedastic time series models. Ann Statist. 2006;34:994–1012. doi: 10.1214/009053606000000191
   Web of Science ®Google Scholar
• Ghoudi K, Rémillard B. Comparison of specification tests for GARCH models. Comput Statist Data Anal. 2014;76:291–300. doi: 10.1016/j.csda.2013.03.009
   Web of Science ®Google Scholar
• Jiménez-Gamero MD. On the empirical characteristic function process of the residuals in GARCH models and applications. Test. 2014;23:409–432. doi: 10.1007/s11749-014-0359-5
   Web of Science ®Google Scholar
• Rémillard B. Specification tests for dynamic models using multipliers. Technical Report; 2012. SSRN Working Paper Series No. 2028558.
   Google Scholar
• Burke MD. Multivariate tests-of-fit and uniform confidence bands using a weighted bootstrap. Statist Probab Lett. 2000;46:13–20. doi: 10.1016/S0167-7152(99)00082-6
   Web of Science ®Google Scholar
• Kojadinovic I, Yan J. Goodness-of-fit testing based on a weighted bootstrap: a fast large sample alternative to the parametric bootstrap. Canad J Statist. 2012;40:480–500. doi: 10.1002/cjs.11135
   Web of Science ®Google Scholar
• Jiménez-Gamero MD, Kim HM. Fast goodness-of-fit tests based on the characteristic function. Comput Statist Data Anal. 2015;89:172–191. doi: 10.1016/j.csda.2015.03.015
   Web of Science ®Google Scholar
• Engle RF. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica. 1982;50:987–1007. doi: 10.2307/1912773
   Web of Science ®Google Scholar
• Bougerol P, Picard N. Strict stationarity of generalized autoregressive process. Ann Probab. 1992;52:115–127.
   Google Scholar
• Bougerol P, Picard N. Stationarity of GARCH processes and of some nonnegative time series. J Econometrics. 1992;20:1714–1730.
   Google Scholar
• Peng L, Yao Q. Least absolute deviations for ARCH and GARCH models. Biometrika. 2003;90:967–975. doi: 10.1093/biomet/90.4.967
   Web of Science ®Google Scholar
• Delhing H, Mikosch T. Random quadratic forms and the bootstrap for U-statistics. J Multivariate Anal. 1994;51:392–413. doi: 10.1006/jmva.1994.1069
   Web of Science ®Google Scholar
• Hušková M, Janssen P. Consistency of the generalized bootstrap for degenerate U-statistics. Ann Statist. 1993;21:1811–1823. doi: 10.1214/aos/1176349399
   Web of Science ®Google Scholar
• Feller W. An introduction to probability theory and its applications, Vol. 2. New York: Wiley; 1971.
   Google Scholar
• Meintanis SG, Jiménez-Gamero MD, Alba-Fernández V. A class of goodness-of-fit tests based on transformation. Comm Statist Theory Methods. 2014;43:1708–1735. doi: 10.1080/03610926.2012.673673
   Web of Science ®Google Scholar
• Epps TW, Pulley LB. A test for normality based on the empirical characteristic function. Biometrika. 1983;70:723–726. doi: 10.1093/biomet/70.3.723
   Web of Science ®Google Scholar
• Jiménez-Gamero MD, Alba-Fernández V, Muñoz-García J, et al. Goodness-of-fit tests based on empirical characteristic functions. Comput Statist Data Anal. 2009;53:3957–3971. doi: 10.1016/j.csda.2009.06.001
   Web of Science ®Google Scholar
• Azzalini A. A class of distributions which includes the normal ones. Scand J Statist. 1985;12:171–178.
   Web of Science ®Google Scholar
• Azzalini A, Capitanio A. The skew-normal and related families. IMS monographs series, New York: Cambridge University Press; 2014.
   Google Scholar
• Rydberg TH. Realistic statistical modelling of financial data. Int Stat Rev. 2000;68:233–258. doi: 10.1111/j.1751-5823.2000.tb00329.x
   Web of Science ®Google Scholar
• Azzalini A, Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J R Stat Soc B. 2003;65:367–389. doi: 10.1111/1467-9868.00391
   Google Scholar
• Francq C, Wintenberger O, Zakoïan JM. GARCH models without positivity constraints: exponential or log GARCH? J Econometrics. 2013;177:34–46. doi: 10.1016/j.jeconom.2013.05.004
   Web of Science ®Google Scholar
• Francq C, Zakoïan JM. GARCH models: structure statistical, inference and applications. London: Wiley; 2010.
   Google Scholar
• Engle RF, Russell JR. Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica. 1998;66:1127–1162. doi: 10.2307/2999632
   Web of Science ®Google Scholar
• Kosorok MR. Introduction to empirical processes and semiparametric inference. New York: Springer; 2008.
   Google Scholar
• Billingsley P. Convergence of probability measures. New York: Wiley; 1968.
   Google Scholar
• Henze N, Hlávka Z, Meintanis SG. Testing for spherical symmetry via the empirical characteristic function. Statistics. 2014;48:1282–1296. doi: 10.1080/02331888.2013.832764
   Web of Science ®Google Scholar
• Newey WK, McFadden D. Large sample estimation and hypothesis testing. In: Engle R, McFadden D, editors. Handbook of econometrics, vol. IV. Amsterdam: North-Holland; 1994. p. 2112–2245.
   Google Scholar