超高次元時系列における予測および情報抽出の方法

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In the areas such as earth science, economics, finance, marketing, life science and environmental science, huge amount of data are being obtained. To develop tools for the extraction of useful information from these massive data, we performed research on the computational methods for fitting multivariate time series with very high-dimension, various sequential filtering algorithms and a method of detecting cosal relation between variables based on estimated multivariate time series model. The methods were applied various problems in real word. The major outcomes are as follows :1.Development of methods for fitting high-dimensional AR model.By using forward and backward prediction error sequences, a very efficient method for estimating AR coefficient matrices was developed. An algorithm for efficient computation on parallel processor is also developed.1.Filtering algorithms for high-dimensional state-space modelTo develop an efficient filtering method that can be applied very-dimensiona … More l state-space models, various algorithms based on information matrices, square-root algorithm, innovation type algorithm and approximation methods were considered. For the extension to nonlinear non-Gaussian state-space models, a new method of performing Gaussian-mixture approximation is also developed.2.Parallel Monte Carlo filter was developed for efficient sequential Monte Carlo filtering for complex problems based on parallel execution of many MCF. By numerical experiments, it was shown that the developed algorithm is very suitable for parallel computation and still maintains equivalent accuracy.3.Applications to real-world problems(1)A method of computing generalized power contribution from estimated AR model was modified and applied to various data sets such as electric power plant data and CDS (credit default swap) data and obtained useful information.(2)By the modeling from high-dimensional time series obtained from ocean bottom seismograph array, analysis method for underground structure was developed. Less