Abstract
Language | English |
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Pages | 1341–1360 |
Number of pages | 20 |
Journal | Science China Mathematics |
Volume | 57 |
Issue number | 7 |
Early online date | 11 Apr 2014 |
DOIs | |
Publication status | Published - 1 Jul 2014 |
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Keywords
- non-stationary TGARCH
- normal mixture QMLE
- asymptotic normality
- consistency
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Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models. / Wang, Hui; Pan, Jiazhu.
In: Science China Mathematics, Vol. 57, No. 7, 01.07.2014, p. 1341–1360.Research output: Contribution to journal › Article
TY - JOUR
T1 - Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models
AU - Wang, Hui
AU - Pan, Jiazhu
PY - 2014/7/1
Y1 - 2014/7/1
N2 - The threshold GARCH (TGARCH) models have been very useful for analyzing asymmetric volatilities arising from financial time series. Most research on TGARCH has been directed to the stationary case. This paper studies the estimation of non-stationary first order TGARCH models. Restricted normal mixture quasi-maximum likelihood estimation (NM-QMLE) for non-stationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter. We show that the proposed estimators (except location parameter) are consistent and asymptotically normal under mild regular conditions. The impact of relative leptokursis and skewness of the innovations’ distribution and quasi-likelihood distributions on the asymptotic efficiency has been discussed. Numerical results lend further support to our theoretical results. Finally, an illustrated real example is presented.
AB - The threshold GARCH (TGARCH) models have been very useful for analyzing asymmetric volatilities arising from financial time series. Most research on TGARCH has been directed to the stationary case. This paper studies the estimation of non-stationary first order TGARCH models. Restricted normal mixture quasi-maximum likelihood estimation (NM-QMLE) for non-stationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter. We show that the proposed estimators (except location parameter) are consistent and asymptotically normal under mild regular conditions. The impact of relative leptokursis and skewness of the innovations’ distribution and quasi-likelihood distributions on the asymptotic efficiency has been discussed. Numerical results lend further support to our theoretical results. Finally, an illustrated real example is presented.
KW - non-stationary TGARCH
KW - normal mixture QMLE
KW - asymptotic normality
KW - consistency
UR - http://link.springer.com/article/10.1007%2Fs11425-014-4815-1
U2 - 10.1007/s11425-014-4815-1
DO - 10.1007/s11425-014-4815-1
M3 - Article
VL - 57
SP - 1341
EP - 1360
JO - Science China Mathematics
T2 - Science China Mathematics
JF - Science China Mathematics
SN - 1674-7283
IS - 7
ER -