Research on Statistical Theory and Time Series Analysis for Mathematical Finance

1.在金融经济时间序列分析中，对协整系统进行了短期因果关系检验和长期因果关系检验。2.建立了大协整系统的预测方法。它是通过提取一个大的协整系统的主成分。通过对25家上市公司股票价格的实证分析和实际预测，验证了该方法的有效性。3.针对包括金融数据在内的经济时间序列，提出了基于拉格朗日乘子的长期持续性检验方法。研究了试验的统计学特性。4.提出了嵌入式完全市场的概念，以取代传统的、但具有限制性的“完全市场”。在此基础上，推导出了一种新的期权定价方法。5.研究了天气衍生产品的定价问题。具体而言，基于东京和名古屋的数据建立了温度模型，以推导出天气导数。6.研究了两种模拟方法，一种是贝氏马尔可夫链蒙特卡罗（MCMC）方法，另一种是非贝叶斯自助法。进一步，将分析扩展到分解的基线数据和惊喜数据。8.研究了分数布朗运动的二次泛函分布的推导。虽然精确的结果没有解决，但给出了一些解释。9.研究了非平稳或长记忆时间序列参数估计的传统时域和频域方法，并与基于小波的估计方法进行了比较。结果表明，基于小波变换的方法比传统的方法具有更高的精度。

1.For analysis of financial and economic time series, the tests for the short-run and the long-run causalities were developed for cointegrated systems.2.The forecasting procedure for large cointegrated systems was developed. It was made possible by extracting principal components of a large cointegrated system. The experiments and the actual forecasts of stock prices of 25 companies supported its validity.3.For analysis of economic time series including financial series, the Lagrange Multiplier test was developed for a change in long-run persistence. Statistical properties of the test were investigated. The strength of persistence in Yen/Dollar exchange rate was examined.4.The new concept, the embedded complete market, was proposed in place of the traditional but restrictive "complete market." Based upon it, a new method for calculating the option price was derived.5.The pricing of the weather derivative was investigated. Specifically, the model for temperature was developed based upon data of Tokyo and Nagoya in order to derive the weather derivative.6.Two simulation methods were investigated for econometric model analysis : One was the Beyesian Markov Chain Monte Carlo(MCMC) method, and the other one was non-Bayes bootstrap method.7.Using the high frequency exchange rate data, the announcement effect of economic indicators was analyzed. Further, the analysis was extended for decomposed baseline data and surprise data.8.Derivation of the distribution for quadratic functionals of fractional Brownian motion was examined. While the exact results were unsolved, some conjectures were given. The prediction on a simple result for moments was obtained.9.After investigating the traditional time-domain and frequency-domain approaches for parameter estimation in non-stationary or long memory time series, they were compared with the wavelet-based estimators. It was found that the wavelet-based method gives more accurate results than the traditional ones.