Statistical inference for nonlinear dynamic model by Markov chain Monte Carlo method
| Project/Area Number |
15500181
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The University of Tokyo |
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Principal Investigator |
OMORI Yasuhiro The University of Tokyo, Faculty of Economics, Associate Professor, 大学院・経済学研究科, 助教授 (60251188)
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| Co-Investigator(Kenkyū-buntansha) |
WAGO Hajime Nagoya University, Department of Economics, Professor, 大学院・経済学研究科, 教授 (00091934)
WATANABE Toshiaki Tokyo Metropolitan University, Faculty of Economics, Professor, 経済学部, 教授 (90254135)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2004: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2003: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Markov chain Monte Carlo / latent variable / Stochastic volatility model / Dynamic Model / Bayesian approach / Random effect / ベイズ推定 / 非線形モデル |
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| Research Abstract |
In the econometric analysis of macroeconomic data, dynamic structures of individual characteristics or unobserved variables have been ignored since microeconomic data were not easily available and these random effects are also considered to be cancelled out after aggregating microeconomic data. However, it has been pointed out that ignoring these random effects or unobserved variables (latent variables) would lead to the bias in the estimation of model parameters. Recently, microeconomic data have started to become disclosed such as panel data which describes dynamic structure of individual characteristics. Using these microeconomic data, we are able to model true structure of individual economic behavior. Various econometric models are proposed to deal with dynamic modeling of latent variables since 1999's.
When there are many latent variables, the conventional maximum likelihood estimation requires the repeated evaluations of highly multidimensional numerical integration. We need to u
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se supercomputers to conduct such computations or we have to approximate the likelihood at the expense of computational accuracies. There are even some cases in which the numerical maximization step fails to converge to the maximum of the likelihood functions. Although alternative approaches such as GEE or GMM methods have been proposed to estimate these models based on methods which are robust to the existence of latent variables, those estimation methods are known to be inefficient.
In this project, we take Bayesian approach and proposed efficient Markov chain Monte Carlo (MCMC) estimation method for various statistical and econometric nonlinear dynamic models. To obtain marginal posterior distribution of model parameters, the MCMC estimation method is known to provide accurate multidimensional integration using simulation method. The MCMC method is computer intensive, but these computations can be done by PC's (note that we do not need supercomputers). When there exist latent variables in the models or we introduce auxiliary variables (for the data augmentation method), the convergence of MCMC samples to the target distribution (posterior distribution) may even be accelerated in some models.
We considered various nonlinear dynamic models : duration models for business cycle dependence, stochastic volatility model with leverage effects, Markov switching and heavy-tailed errors (based on mixture of normal distributions), and stochastic volatility model for foreign exchange markets. We first proposed simple sampling methods (such as single-move sampler which samples one parameter at a time) for these models and elaborate the multi-move samplers (which samples a block of parameters) to improve the speed of the convergence to the target posterior distributions. Less
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Report
(3 results)
Research Products
(48 results)
