An introduction to time series modeling / Andreas Jakobsson

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Introduction -- Stochastic vectors -- Stochastic processes -- Identification and modeling -- Estimation and testing -- Prediction of stochastic processes -- Multivariate processes -- Tracking dynamic systems -- Some useful formulae -- Probability distributions

Time series analysis concerns the mathematical modeling of time varying phenomena, e.g., ocean waves, water levels in lakes and rivers, demand for electrical power, radar signals, muscular reactions, ECG-signals, or option prices at the stock market. This book gives a comprehensive presentation of stochastic models and methods in time series analysis. The book treats stochastic vectors and both univariate and multivariate stochastic processes, as well as how these can be used to identify suitable models for various forms of observations. Furthermore, different approaches such as least squares, the prediction error method, and maximum likelihood are treated in detail, together with results on the Cramér-Rao lower bound, dictating the theoretically possible estimation accuracy. Residual analysis and prediction of stochastic models are also trated, as well as how one may form time-varying models, including the recursive least squares and the Kalman filter. The book discusses how to implement the various methods using Matlab, and several Matlab functions and data sets are provided with the book