A new Pearson-type QMLE for conditionally heteroskedastic models
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 52344.
Date of creation: 18 Dec 2013
Date of revision:
Asymmetric innovation; Conditionally heteroskedastic model; Exchange rates; GARCH model; Leptokurtic innovation; Non-Gaussian QMLE; Pearson's Type IV distribution; Pearsonian QMLE; Stock indexes.;
Other versions of this item:
- Zhu, Ke & Li, Wai Keung, 2014. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52732, University Library of Munich, Germany.
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-12-29 (All new papers)
- NEP-ECM-2013-12-29 (Econometrics)
- NEP-ORE-2013-12-29 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
- Malay Bhattacharyya & Nityanand Misra & Bharat Kodase, 2009. "MaxVaR for non-normal and heteroskedastic returns," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 925-935.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Cheng, Xixin & Li, W.K. & Yu, Philip L.H. & Zhou, Xuan & Wang, Chao & Lo, P.H., 2011. "Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2590-2604, September.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
- 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.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Christan Francq & Jean-Michel Zakoian, 2012.
"Optimal Predictions of Powers of Conditionally Heteroskedastic Processes,"
2012-17, Centre de Recherche en Economie et Statistique.
- Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, 03.
- Francq, Christian & Zakoian, Jean-Michel, 2010. "Optimal predictions of powers of conditionally heteroskedastic processes," MPRA Paper 22155, University Library of Munich, Germany.
- Drost, F.C. & Klaassen, C.A.J., 1997.
"Efficient estimation in semiparametric GARCH models,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-74146, Tilburg University.
- Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
- Drost, F.C. & Klaassen, C.A.J., 1996. "Efficient Estimation in Semiparametric GARCH Models," Discussion Paper 1996-38, Tilburg University, Center for Economic Research.
- Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
- Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
- Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
- Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept.
- Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
- Bauwens, Luc & Laurent, Sebastien, 2005.
"A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 23, pages 346-354, July.
- Tom Doan, . "LOGMVSKEWT: RATS procedure to compute function for log density of multivariate skew-t distribution," Statistical Software Components RTS00107, Boston College Department of Economics.
- BAUWENS, Luc & LAURENT, Sébastien, . "A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models," CORE Discussion Papers RP -1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- Peter Christoffersen & Steve Heston & Kris Jacobs, 2003.
"Option Valuation with Conditional Skewness,"
CIRANO Working Papers
- Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
- Francq, Christian & Wintenberger, Olivier & Zakoian, Jean-Michel, 2012.
"Garch models without positivity constraints: exponential or log garch?,"
41373, University Library of Munich, Germany.
- Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
- Zakoïan, Jean-Michel & Wintenberger, Olivier & Francq, Christian, 2013. "GARCH models without positivity constraints: Exponential or Log GARCH?," Economics Papers from University Paris Dauphine 123456789/10571, Paris Dauphine University.
- Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
- Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
- Guodong Li & Wai Keung Li, 2008. "Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity," Biometrika, Biometrika Trust, vol. 95(2), pages 399-414.
- Andrews, Beth, 2012. "Rank-Based Estimation For Garch Processes," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1037-1064, October.
- Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
- Verhoeven, Peter & McAleer, Michael, 2004.
"Fat tails and asymmetry in financial volatility models,"
Mathematics and Computers in Simulation (MATCOM),
Elsevier, vol. 64(3), pages 351-361.
- Peter Verhoeven & Michael McAleer, 2003. "Fat Tails and Asymmetry in Financial Volatility Models," CIRJE F-Series CIRJE-F-211, CIRJE, Faculty of Economics, University of Tokyo.
- 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.
- Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
- Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-66, December.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.