Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models |
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| Institution: | 1. School of Finance, Central University of Finance and Economics, China;2. Department of Mathematics and Statistics, University of Strathclyde, UK;1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, China;2. School of Economics and Management, Southeast University, Nanjing, 210096, China;3. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania;4. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius LT-08663, Lithuania;1. Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th street, PH C104, Bloomington, IN, 47405, USA;2. Department of Epidemiology and Biostatistics, University of Georgia, Athens, GA 30602, USA;3. Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, PO Box 750332, Dallas, TX 75275-0332, USA;1. Université de Rouen, LITIS EA 4108, Avenue de l’Université, BP 12, 76801 Saint-Étienne-du-Rouvray, France;2. Rutgers University, Department of Statistics, 561 Hill Center, Busch Campus, Piscataway, NJ 08854-8019, USA;1. Clausthal University of Technology, Department of Applied Stochastics and Operations Research, 38678 Clausthal-Zellerfeld, Germany;2. University of Derby, School of Computing and Mathematics, Derby, DE22 1GB, UK |
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| Abstract: | Although quasi maximum likelihood estimator based on Gaussian density (G-QMLE) is widely used to estimate GARCH-type models, it does not perform successfully when error distribution is either skewed or leptokurtic. This paper proposes normal mixture quasi-maximum likelihood estimator (NM-QMLE) for non-stationary TGARCH(1,1) models. We show that, under mild regular conditions, there is no consistent estimator for the intercept, and the proposed estimator for any other parameter is consistent. |
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| Keywords: | Non-stationary TGARCH models NM-QMLE Consistency |
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