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Inference for 2-D GARCH models |
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| Institution: | 1. Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul, 110-745, Republic of Korea;2. Mathematics Department, Tulane University, 6823 St. Charles Avenue, New Orleans, LA 70118, USA;3. Department of Statistics and Operations Research, UNC at Chapel Hill, CB#3260, Hanes Hall, Chapel Hill, NC 27599, USA;1. Loughborough University, Department of Mathematical Sciences, Loughborough, Leicestershire, LE11 3TU, UK;2. University of Strathclyde, Department of Mathematics and Statistics, Glasgow, G1 1XH, UK;3. School of Economics and Management, Fuzhou University, China |
| Abstract: | The purpose of this paper is, in the first step, to consider a class of GMM estimators with interesting asymptotic properties and a reasonable number of computations for two dimensionally indexed Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. In the second step, we use the central limit theorem of Huang (1992) for spatial martingale differences to establish the LAN property for general two-dimensional discrete models on a regular grid with Gaussian errors. We then apply this result to the spatial GARCH model and derive the limit distribution of the maximum likelihood estimators of the parameters. Results of numerical simulations are presented. |
| Keywords: | Spatial model Nonlinear interdependency Local asymptotic normality Maximum likelihood estimation Heteroscedasticity |
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