Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model
AbstractEfficient GMM estimation of the semi-strong GARCH(1,1) model requires simultaneous estimation of the conditional third and fourth moments. This paper proposes a simple alternative to efficient GMM based upon the unconditional skewness of residuals and the autocovariances of squared residuals. An advantage of this simple alternative is that neither the third nor the fourth conditional moment needs to be estimated. A second advantage is that linear estimators apply to all of the parameters in the model, making estimation straightforward in practice. The proposed estimators are IV-like with potentially many instruments. Sequential estimation involves TSLS in a first step followed by linear GMM. Simultaneous estimation involves either two-step GMM or CUE. A Monte Carlo study of the proposed estimators is included.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 20034.
Date of creation: Jan 2010
Date of revision:
GARCH; Time Series Heteroskedasticity; GMM; CUE; Many Moments; Conditional Moment Restrictions; Consistency; Robust Statistics;
Find related papers by JEL classification:
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-23 (All new papers)
- NEP-ECM-2010-01-23 (Econometrics)
- NEP-ETS-2010-01-23 (Econometric Time Series)
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- Rich, Robert W. & Raymond, Jennie & Butler, J. S., 1991. "Generalized instrumental variables estimation of autoregressive conditional heteroskedastic models," Economics Letters, Elsevier, vol. 35(2), pages 179-185, February.
- 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.
- Chirok Han & Peter C.B. Phillips, 2005.
"GMM with Many Moment Conditions,"
Cowles Foundation Discussion Papers
1515, Cowles Foundation for Research in Economics, Yale University.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
- Taskinen, Sara & Oja, Hannu & Randles, Ronald H., 2005. "Multivariate Nonparametric Tests of Independence," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 916-925, September.
- Drost, Feike C & Nijman, Theo E, 1993.
"Temporal Aggregation of GARCH Processes,"
Econometric Society, vol. 61(4), pages 909-27, July.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153273, Tilburg University.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
- 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.
- Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
- Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
- Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-63, May.
- Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
- 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.
- MEDDAHI, Nour & RENAULT, Éric, 1998.
"Quadratic M-Estimators for ARCH-Type Processes,"
Cahiers de recherche
9814, Universite de Montreal, Departement de sciences economiques.
- Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Escanciano, Juan Carlos, 2009. "Quasi-Maximum Likelihood Estimation Of Semi-Strong Garch Models," Econometric Theory, Cambridge University Press, vol. 25(02), pages 561-570, April.
- Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2009.
"Merits and drawbacks of variance targeting in GARCH models,"
15143, University Library of Munich, Germany.
- Christian Francq & Lajos Horváth, 2011. "Merits and Drawbacks of Variance Targeting in GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(4), pages 619-656.
- Christian FRANCQ & Lajos HORVATH & Jean-Michel ZAKOIAN, 2009. "Merits and Drawbacks of Variance Targeting in GARCH Models," Working Papers 2009-17, Centre de Recherche en Economie et Statistique.
- 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).
- White, Halbert, 1982. "Instrumental Variables Regression with Independent Observations," Econometrica, Econometric Society, vol. 50(2), pages 483-99, March.
- Andrews, Donald W. K., 1987.
"Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables,"
645, California Institute of Technology, Division of the Humanities and Social Sciences.
- Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
- Peter A. Zadrozny, 2005. "Necessary and Sufficient Restrictions for Existence of a Unique Fourth Moment of a Univariate GARCH(p,q) Process," CESifo Working Paper Series 1505, CESifo Group Munich.
- Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
- Mark, Nelson C., 1988. "Time-varying betas and risk premia in the pricing of forward foreign exchange contracts," Journal of Financial Economics, Elsevier, vol. 22(2), pages 335-354, December.
- Skoglund, Jimmy, 2001. "A simple efficient GMM estimator of GARCH models," Working Paper Series in Economics and Finance 0434, Stockholm School of Economics.
- Asger Lunde & Peter Reinhard Hansen, 2001.
"A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?,"
2001-04, Brown University, Department of Economics.
- Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
- 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.
- 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.
- Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
- Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
- Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
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