Theory construction of asymptotic statistics for stochastic processes and its application to high-frequency data analysis

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Mainly, we have derived the following devices concerning statistical analyses for the stochastic process models : (1) how to estimate the parameters and construct their approximate confidence regions, when the model exhibits heteroskedasticity ; (2) sets of sufficient conditions for the long-term stability of the models ; (3) an easy-to-implement and precise method for estimating the mean structure, when the model is of pure-jump type ; (4) test statistics for the noise normality, enabling us to avoid a serious model misspecification. All of these results can serve as tool for an efficient and quantitative exploitation of underlying information.