Electrical engineering Time series prediction using Kalman filter R and state space model (statistics One Point 2

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Electrical Engineering
Politics, Economy, and Society
The Kalman filter was originally proposed as a dynamic system control method in the engineering field. Since then, the usefulness of the Kalman filter as a time series analysis method has been found. Various derivatives have been created and its application range has been expanded. There are many situations in which time series data are analyzed and predicted. There is a state space model as a framework of a flexible time series model which can respond to the needs of various time series analysis. A calculation method which gives estimation of a state space model at high speed by a computer is the Kalman filter. This paper explains a methodology of time series analysis mainly using the Kalman filter and a practice of data analysis. Especially, using free software R for statistics. Many pages are devoted to analysis examples of various time series and examples of concrete analysis codes. Analysis examples for familiar data are also included. Analysis examples for familiar data are also included. First, as a preliminary preparation, the following are explained : Multivariate probability distribution and basic knowledge of time series, and representative time series models. Then, state space models are introduced. Local level models which are the most basic state space models, and state space models in which linear models and normal (Gaussian) distributions are assumed are treated. Non-Gaussian state space models in which observation distributions are extended to non-normal distributions for those models are treated. Then, Kalman filter is introduced as an analysis method. Finally, non-linear and non-Gaussian state space models are treated. Particle filters are introduced as an analysis method. As the chapter advances, the model to be handled becomes more generalized. The contents are sufficient for undergraduate students, graduate students, and members of society who have mastered the basis of probability and statistics. By this book, even practical analyses using state space models and Kalman filters can be acquired.