Statistical inference for extended models in financial time series

研究了金融时间序列统计分析中的问题。由于经典的统计理论和方法无法解决这些问题，计量经济学中出现了一个新的研究领域。作为结果，相应的理论和方法已被开发的问题有关的关键字列出如下。但即使是现在，我们认为与多个关键字相关的复合问题仍然存在许多未解决的问题，例如与Gestival误差相关的向量误差校正模型的估计问题，Gestival过程中的长记忆，高频数据的结构变化，利用高频时间序列对已实现波动率进行建模等问题进行了研究，并取得了一些有意义的结果，提出了一些适用于实际波动率建模的方法，解决这些新问题的方法。此外，我们通过计算机模拟评估了我们的理论和方法的结果，并将其应用于真实的数据。

We studied problems in statistical analysis of financial time series. Since those problems cannot be dealt with classical statistical theory and methods a new research field in econometrics has emerged. As the results the appropriate theory and methods have been developed for problems concerning to the keyword listed below. But even now we think there remain many unsolved problems for compound problems related to plural keywords, such as estimation problems related to vector error correction model with GARCH error, long memory in GARCH process, structural change in high frequency data, modeling of realized volatility by using high frequency time series and so on. We challenged to such problems and attained some significant results including a proposal of some suitable method to such new problems. In addition we evaluated our theoretical and methodological results by computer simulation and applied them to real data.