Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models

Hui Wang, Jiazhu Pan

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages1341–1360
Number of pages20
JournalScience China Mathematics
Volume57
Issue number7
Early online date11 Apr 2014
DOIs
Publication statusPublished - 1 Jul 2014

Fingerprint

Normal Mixture
Threshold Model
GARCH Model
Generalized Autoregressive Conditional Heteroscedasticity
Location Parameter
Quasi-maximum Likelihood
Quasi-likelihood
Asymptotic Efficiency
Financial Time Series
Skewness
Maximum Likelihood Estimation
Volatility
Model
First-order
Estimator
Numerical Results
Estimate

Keywords

  • non-stationary TGARCH
  • normal mixture QMLE
  • asymptotic normality
  • consistency

Cite this

Wang, Hui ; Pan, Jiazhu. / Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models. In: Science China Mathematics. 2014 ; Vol. 57, No. 7. pp. 1341–1360.
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Wang, H & Pan, J 2014, 'Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models' Science China Mathematics, vol. 57, no. 7, pp. 1341–1360. https://doi.org/10.1007/s11425-014-4815-1

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

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T1 - Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models

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AU - Pan, Jiazhu

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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.

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Wang H, Pan J. Restricted normal mixture QMLE for non-stationary TGARCH(1, 1) models. Science China Mathematics. 2014 Jul 1;57(7):1341–1360. https://doi.org/10.1007/s11425-014-4815-1

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