Zhu, Ke and Li, Wai Keung (2013): A new Pearson-type QMLE for conditionally heteroskedastic models.
Preview |
PDF
MPRA_paper_52344.pdf Download (650kB) | Preview |
Abstract
This paper proposes a novel Pearson-type quasi maximum likelihood estimator (QMLE) of GARCH($p, q$) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not the heavy-tailed but also the skewed innovations. Under the stationarity and weak moment conditions, the strong consistency and asymptotical normality of the PQMLE are obtained. With no further efforts, the PQMLE can apply to other conditionally heteroskedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to eight major stock indexes and four exchange rates further highlight the importance of our new method. To our best knowledge, the heavy-tailed and skewed innovations are observed together in practice, and the PQMLE now gives us a systematical way to capture this co-existing feature.
Item Type: | MPRA Paper |
---|---|
Original Title: | A new Pearson-type QMLE for conditionally heteroskedastic models |
English Title: | A new Pearson-type QMLE for conditionally heteroskedastic models |
Language: | English |
Keywords: | Asymmetric innovation; Conditionally heteroskedastic model; Exchange rates; GARCH model; Leptokurtic innovation; Non-Gaussian QMLE; Pearson's Type IV distribution; Pearsonian QMLE; Stock indexes. |
Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics |
Item ID: | 52344 |
Depositing User: | Dr. Ke Zhu |
Date Deposited: | 18 Dec 2013 19:50 |
Last Modified: | 13 Oct 2019 21:30 |
References: | ANDREWS, B. (2012). Rank-based estimation for GARCH processes. Econometric Theory 28, 1037-1064. BAI, X., RUSSELL, J.R. & TIAO, G.C. (2003). Kurtosis of GARCH and stochastic volatility models with non-normal innovations. Journal of Econometrics 114, 349–360. BAUWENS, L. & LAURENT, S. (2005). A New Class of Multivariate Skew Densities, with Application to Generalized Autoregressive Conditional Heteroscedasticity Models. Journal of Business & Economic Statistics 23, 346–354. BERA, A.K. & HIGGINS, M.L. (1993). ARCH models: Properties, estimation and testing. Jounal of Economic Surveys 7, 305-366; reprinted in Surveys in Econometrics (L. Oxley et al., eds.) 215-272. Blackwell, Oxford 1995. BERKES, I., HORVATH, L. & KOKOSZKA, P. (2003) GARCH processes: Structure and estimation. Bernoulli 9, 201-227. BOUGEROL, P. & PICARD, N. (1992). Stationarity of GARCH processes and of some nonnegative time series. Journal of Econometrics 52, 115-127. BERKES, I. & HORVA TH, L. (2004). The efficiency of the estimators of the parameters in GARCH processes. Annals 375 of Statistics 32, 633-655. BHATTACHARYYA, M., MISRA, N. & KODASE, B. (2009). MaxVaR for non-normal and heteroskedastic returns. Quantitative Finance 9, 925–935. BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-327. 380 BOLLERSLEV, T. (1987). A conditionally heteroskedastic time series model for speculative prices and rates of return. The Review of Economics and Statistics 69, 542-547. BOLLERSLEV, T., CHOU, R.Y. & KRONER, K.F. (1992). ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5-59. BOLLERSLEV, T. & WOOLDRIDGE, J.M. (1992). Quasi-maximum likelihood estimation of dynamic models with 385 time varying covariance. Econometric Reviews 11, 143–172. CHEN, M. & ZHU, K. (2013). Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations. Working paper. Chinese Academy of Sciences. CHRISTOFFERSEN, P., HESTON, S. & JACOBS, K. (2006). Option valuation with conditional skewness. Journal of Econometrics 131, 253-284. DING, Z., GRANGER, C.W.J. & ENGLE, R.F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83-106. DROST, F.C. & KLAASSEN, C.A.J. (1997). Efficient estimation in semiparametric garch models. Journal of Econometrics 81, 193-221. ENGLE, R.F. (1982). Autoregressive conditional heteroskedasticity with estimates of variance of U.K. inflation. Econometrica 50, 987-1008. ENGLE, R.F. & GONZ´ALEZ-RIVERA, G. (1991). Semiparametric arch models. Journal of Business and Economic Statistics 9, 345-359. GRIGOLETTO, M. & LISI, F. Looking for skewness in financial time series. Econometrics Journal 12, 310-323. HANSEN, B.E. (1994). Autoregressive conditional density estimation. International Economic Review 35, 705-730. HARVEY, C.R. & SIDDIQUE, A. (1999). Autoregressive conditional skewness. Journal of Financial and Quantitative Analysis 34, 465-487. HEINRICH, J. (2004). A guide to the Pearson type IV distribution. Working paper. University of Pennsylvania. FAN, J., QI, L. & XIU, D. (2013). Quasi maximum likelihood estimation of GARCH models with heavy-tailed likelihoods. Journal of Business and Economic Statistics. forthcoming. FRANCQ, C., WINTENBERGER, O. & ZAKO¨I 405 AN, J.M. (2013). Garch models without positivity constraints: exponential or log garch? Journal of Econometrics. forthcoming. FRANCQ, C. & ZAKOIAN, J.M. (2004). Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes. Bernoulli 10, 605-637. FRANCQ, C. & ZAKOIAN, J.M. (2010). GARCH Models: Structure, Statistical Inference and Financial Applications. 410 Wiley, Chichester, UK. FRANCQ, C. & ZAKOIAN, J.M. (2013). Optimal predictions of powers of conditionally heteroscedastic processes. Journal of the Royal Statistical Society B 75, 345-367. GEWEKE, J. (1986). Modeling the persistence of conditional variances: A comment. Econometric Review 5, 57-61. HAMADEH, T. & ZAKOIAN, J.M. (2011). Asymptotic properties of LS and QML estimators for a class of nonlinear GARCH processes. Journal of Statistical Planning and Inference 141, 488-507. HALL, P. & YAO, Q. (2003). Inference in ARCH and GARCH models with heavy-tailed errors. Econometrica 71, 285-317. JONDEAU, E. & ROCKINGER, M. (2001). Gram-Charlier densities. Journal of Economic Dynamics and Control 25, 1457-1483. LING, S. (2007). Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models. Journal of Econometrics 140, 849-873. LIU, S.-M. & BRORSEN, B.W. (1995). Maximum likelihood estimation of a GARCH-stable model. Journal of applied econometrics 10, 273–285. NAGAHARA, Y. (1999). The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters. 425 Statistics & Probability Letters 43, 251-264. NELSON, D.B. (1990). Stationarity and persistence in the GARCH(1,1) model. Econometric Theory 6, 318-334. NELSON, D.B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59, 347-370. NEWEY, W.K. & STEIGERWALD, D.G. (1997). Asymptotic bias for quasi-maximum likelihood estimators in conditional heteroskedasticity models. Econometrica 65, 587-599. PENG, L. & YAO, Q. (2003). Least absolute deviations estimation for ARCH and GARCH models. Biometrika 90, 967-975. PREMARATNE, G. & BERA, A.K. (2001). Modeling asymmetry and excess kurtosis in stock return data. Working paper. University of Illinois. YAN, J. (2005). Asymmetry, fat-tail, and autoregressive conditional density in fincancial return data with systems of frequency curves. Working paper. University of Iowa. VERHOEVEN, P. MCALEER, M. (2004). Fat tails and asymmetry in financial volatility models. Mathematics and Computers in Simulation 64, 351-361. ZHU, K. & LING, S. (2011). Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models. Annals of Statistics 39, 2131-2163. ZHU, K. & LING, S. (2013). Inference for ARMA models with unknown-form and heavy-tailed G/ARCH-type noises. Working paper. Hong Kong University of Science and Technolegy. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/52344 |