Research on Statistical Theory and Time Series Analysis for Mathematical Finance

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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.