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  • Rong Liu (a1) and Lijian Yang (a2)

The semiparametric GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) model of Yang (2006, Journal of Econometrics 130, 365–384) has combined the flexibility of a nonparametric link function with the dependence on infinitely many past observations of the classic GARCH model. We propose a cubic spline procedure to estimate the unknown quantities in the semiparametric GARCH model that is intuitively appealing due to its simplicity. The theoretical properties of the procedure are the same as the kernel procedure, while simulated and real data examples show that the numerical performance is either better than or comparable to the kernel method. The new method is computationally much more efficient than the kernel method and very useful for analyzing large financial time series data.

Corresponding author
*Address correspondence to Lijian Yang, Center for Advanced Statistics and Econometrics Research, Soochow University, Suzhou 215006, China; e-mail:
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Y. Baraud , F. Comte , & G. Viennet (2001) Model selection for (auto-)regression with dependent data. ESAIM: Probability and Statistics 5, 3349.

L. Bauwens , B. Laurent , & J. Rombouts (2006) Multivariate GARCH models: A survey. Journal of Applied Econometrics 21, 79109.

L.D. Brown & M. Levine (2007) Variance estimation in nonparametric regression via the difference sequence method. Annals of Statistics 35, 22192232.

M. Carrasco & X. Chen (2002). Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 1739.

N. Chan , S. Deng , L. Peng , & Z. Xia (2007) Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations. Journal of Econometrics 137, 556576.

C.M. Dahl & M. Levine (2006) Nonparametric estimation of volatility models with serially dependent innovations. Statistics and Probability Letters 76, 20072016.

C de Boor . (2001) A Practical Guide to Splines. Springer-Verlag.

R.F. Engle & V. Ng (1993) Measuring and testing the impact of news on volatility. Journal of Finance 48, 17491778.

L.R. Glosten , R. Jaganathan , & D.E. Runkle (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 17791801.

C.M. Hafner & H. Herwartz (2006) Volatility impulse responses for multivariate GARCH models: An exchange rate illustration. Journal of International Money and Finance 25, 719740.

C.M. Hafner & O. Linton (2010) Efficient estimation of a multivariate multiplicative volatility model. Journal of Econometrics 159, 5573.

L Hentschel . (1995) All in the family: Nesting symmetric and asymmetric GARCH models. Journal of Financial Economics 39, 71104.

J.Z Huang . (2003) Local asymptotics for polynomial spline regression. Annals of Statistics 31, 16001635.

J.Z. Huang & L. Yang (2004) Identification of nonlinear additive autoregressive models. Journal of the Royal Statistical Society Series B 66, 463477.

M Levine . (2006) Bandwidth selection for a class of difference-based variance estimators in the nonparametric regression: A possible approach. Computational Statistics and Data Analysis 50, 34053431.

O. Linton & E. Mammen (2005) Estimating semiparametric ARCH(∞) models by kernel smoothing methods. Econometrica 73, 771836.

L. Peng & Q. Yao (2003) Least absolute deviations estimation for ARCH and GARCH models. Biometrika 90, 967975.

A. Silvennoinen & T. Teräsvirta (2009) Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH model. Journal of Financial Econometrics 7, 373411.

C Stone . (1985) Additive regression and other nonparametric models. Annals of Statistics 13, 689705.

Y. Sun & T. Stengos (2006) Semiparametric efficient adaptive estimation of asymmetric GARCH models. Journal of Econometrics 133, 373386.

L. Wang , C. Feng , Q. Song , & L. Yang (2012) Efficient semiparametric GARCH modelling of financial volatility. Statistica Sinica 22, 249270.

L. Wang & L. Yang (2007) Spline-backfitted kernel smoothing of nonlinear additive autoregression model. Annals of Statistics 35, 24742503.

L Yang . (2006) A semiparametric GARCH model for foreign exchange volatility. Journal of Econometrics 130, 365384.

L. Yang , W. Härdle , & J.P. Nielsen (1999) Nonparametric autoregression with multiplicative volatility and additive mean. Journal of Time Series Analysis 20, 597604.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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