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Published online by Cambridge University Press:  20 March 2015

Rong Liu
Soochow University and University of Toledo
Lijian Yang*
Soochow University
*Address correspondence to Lijian Yang, Center for Advanced Statistics and Econometrics Research, Soochow University, Suzhou 215006, China; e-mail:


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.

Copyright © Cambridge University Press 2015 

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The comments from editor Peter Phillips, co-editor Oliver Linton and two anonymous referees have resulted in substantial improvement of the work. This research has been supported in part by NSF awards DMS 0706518, 1007594, Jiangsu Specially-Appointed Professor Program SR10700111, Jiangsu Province Key-Discipline (Statistics) Program ZY107002, ZY107992, National Natural Science Foundation of China Award NSFC 11371272, Research Fund for the Doctoral Program of Higher Education of China Award 20133201110002.



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