Research on Statistical Theory and Time Series Analysis for Mathematical Finance

数学金融统计理论与时间序列分析研究

基本信息

批准号：
14203003
负责人：
YAMAMOTO Taku
金额：
$ 26.87万
依托单位：
Hitotsubashi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

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.

1.为了分析金融和经济时间序列，开发了协整系统的短期和长期因果关系检验。2.开发了大型协整系统的预测程序。这是通过提取大型协整系统的主要成分而实现的。实验和对25家公司股票价格的实际预测支持了其有效性。3.为了分析包括金融序列在内的经济时间序列，针对长期持久性的变化开发了拉格朗日乘子检验。研究了测试的统计特性。考察了日元/美元汇率的持续性强度。4.提出嵌入式完全市场这一新概念来代替传统但具有限制性的“完全市场”。在此基础上，推导了一种新的期权价格计算方法。5.对天气衍生品的定价进行了研究。具体来说，根据东京和名古屋的数据建立了温度模型，以推导天气导数。6.研究了两种计量经济模型分析的模拟方法：一种是贝耶斯马尔可夫链蒙特卡罗（MCMC）方法，另一种是贝耶斯马尔可夫链蒙特卡罗（MCMC）方法。另一种是非贝叶斯引导法。7.利用高频汇率数据，分析经济指标的公布效果。此外，分析还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。虽然确切的结果尚未确定，但给出了一些猜测。得到了对矩的简单结果的预测。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，并将它们与基于小波的估计器进行了比较。结果发现，基于小波的方法比传统方法给出了更准确的结果。