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	Estimation and tests for power-transformed and threshold GARCH models
	Pan, Jiazhu ; Wang, Hui ; Tong, Howell
	2008
关键词	threshold GARCH power transformation asymptotic normality quasi-maximum likelihood estimator least absolute deviations estimation Wald test order selection PTTGARCH structure ABSOLUTE DEVIATIONS ESTIMATION INFINITE VARIANCE TIME-SERIES ARCH STATIONARITY ERRORS
英文摘要	Consider a class of power-transformed and threshold GARCH(p, q) (PTTGRACH(p, q)) model, which is a natural generalization of power-transformed and threshold GARCH(l, I) model in Hwang and Basawa [2004. Stationarity and moment structure for Box-Cox transformed threshold GARCH(l,l) processes. Statistics & Probability Letters 68, 209-220.] and includes the standard GARCH model and many other models as special cases. We first establish the asymptotic normality for quasi-maximum likelihood estimators (QMLE) of the parameters under the condition that the error distribution has finite fourth moment. For the case of heavy-tailed errors, we propose a least absolute deviations estimation (LADE) for PTTGARCH(p, q) model, and prove that the LADE is asymptotically normally distributed under very weak moment conditions. This paves the way for a statistical inference based on asymptotic normality for heavy-tailed PTTGARCH(p, q) models. As a consequence, we can construct the Wald test for GARCH structure and discuss the order selection problem in heavy-tailed cases. Numerical results show that LADE is more accurate than QMLE for heavy-tailed errors. Furthermore, the theory is applied to the daily returns of the Hong Kong Hang Seng Index, which suggests that asymmetry and nonlinearity could be present in the financial time series and the PTTGARCH model is capable of capturing these characteristics. As for the probabilistic structure of PTTGARCH(p, q) model, we give in the appendix a necessary and sufficient condition for the existence of a strictly stationary solution of the model, the existence of the moments and the tail behavior of the strictly stationary solution. (C) 2007 Elsevier B.V. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000251910600015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Economics; Mathematics, Interdisciplinary Applications; Social Sciences, Mathematical Methods; SCI(E); EI; SSCI; 28; ARTICLE; 1; 352-378; 142
语种	英语
出处	SCI ; EI
出版者	journal of econometrics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157831]
专题	数学科学学院
推荐引用方式 GB/T 7714	Pan, Jiazhu,Wang, Hui,Tong, Howell. Estimation and tests for power-transformed and threshold GARCH models. 2008-01-01.

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