基于自适应建议密度的GARCH模型贝叶斯推理
Bayesian inference with an adaptive proposal density for GARCH models
摘要：
我们执行的GARCH模型的贝叶斯推理的Metropolis-Hastings算法与自适应的建议密度。自适应的建议密度被假定为学生的t分布和分布参数进行评估，通过使用在模拟过程中采样的数据。将该方法应用于非对称GARCH模型中的QGARCH模型，并对日经225指数、DAX指数和恒生指数进行了实证研究。我们发现，我们的方法的自相关时间是非常小的，因此该方法是非常有效的生成不相关的蒙特卡罗数据。QGARCH模型的结果表明，三个指数都表现出杠杆效应，即在负面观察之后波动性很高。
英文摘要：
We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for the QGARCH model which is one of asymmetric GARCH models and make empirical studies for for Nikkei 225, DAX and Hang indexes. We find that autocorrelation times from our method are very small, thus the method is very efficient for generating uncorrelated Monte Carlo data. The results from the QGARCH model show that all the three indexes show the leverage effect, i.e. the volatility is high after negative observations.
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