Various types of decompositions of discrete-time stochastic processes and their applications to time series analysis

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In this research we investigated methods for the analysis of time series (set of data observed over time; e.g. stock prices, seismic waves), especially from the viewpoint of decompositions of discrete-time stochastic processes (such as "Fluctuation-dissipation decomposition", "Trigonometric decomposition" and "White noise decomposition"). These decompositions have potential applications to, e.g., detection of abnormal behavior in time series, classification of time series by extracting their characteristics, and secret sharing schemes for time series. With this in mind, we implemented the algorithms for these decompositions based on the fundamental mathematical research.