Testing Randomess of Heteroskedastic Time Series Data Base of Simulation

本研究是我之前对异方差时间序列数据的序列相关检验工作的延伸。我已经证明了它适用于GARCH-M模型框架下的零风险溢价检验。通过对日本股票指数的分析，表明风险溢价的存在与经济学中一般的风险溢价理论相一致。我还证明了这种方法适用于两个时间序列之间相互关系的检验。在这项工作的过程中，我找到了一种高效生成GARCH样本路径的方法。它有望在未来用于GARCH参数的有效估计。当我们把GARCH模型看作一个马尔可夫过程时，我还发现了分布收敛到极限平衡分布的速度。我还通过经验证明，当采样周期足够长时，GARCH的参数估计是鲁棒的。作为这项工作的副产品，我在二维理性投票理论中找到了一种新的平衡。

This investigation is an extenstion of my previous work on the serial correlation test of heteroskedasitc time series data.I have shown that it is applicable to the test of zero risk-premium in the framework of GARCH-M model. It application to some Japanese stock indices has shown the existence of risk-premium which is consistent with the ordinary risk premium theory in economics.I have also shown that this approach is applicable to the test of cross-correlation between two time series.In the process of this work, I found a method for efficient generation of a GARCH sample path. It is expected to be used for the efficient estimation of GARCH parameters in the future.I have also found the rate of convergence of distribution to the limit equilibrium distribution when we regard the GARCH model as a Markov process.I have also shown empirically that the parameter estimation of GARCH is robust when the sampling period is enough long.As a by-product of this work, I found a new equilibrium in the two dimensional rational voting theory.