This book, "Time Series Analysis by State Space Methods," second edition, by J. Durbin and S. J. Koopman, provides a comprehensive overview of state space methods for time series analysis. It covers both linear and non-linear, as well as non-Gaussian models, and discusses prior knowledge, notation, and other relevant literature. The book begins with the local level model, explaining filtering, smoothing, and forecasting techniques, including the Kalman filter, regression lemma, and Bayesian treatment. It then moves on to linear state space models, discussing univariate and multivariate structural time series models, ARMA and ARIMA models, exponential smoothing, regression models, and dynamic factor models. The text also explores continuous-time state space models, spline smoothing, and further comments on state space analysis, comparing it with Box-Jenkins approaches and benchmarking. The second part of the book focuses on non-Gaussian and non-linear state space models, covering special cases, heavy-tailed distributions, stochastic volatility models, and other financial models. It discusses approximate filtering and smoothing techniques, including the extended Kalman filter, unscented Kalman filter, and nonlinear smoothing. The book also introduces importance sampling for smoothing, particle filtering, and Bayesian estimation of parameters. It includes practical illustrations, such as the Nile data, and provides examples of non-Gaussian and nonlinear models, including Poisson, binary, and heavy-tailed densities. The book concludes with references, author index, and subject index, making it a valuable resource for researchers and practitioners in time series analysis.This book, "Time Series Analysis by State Space Methods," second edition, by J. Durbin and S. J. Koopman, provides a comprehensive overview of state space methods for time series analysis. It covers both linear and non-linear, as well as non-Gaussian models, and discusses prior knowledge, notation, and other relevant literature. The book begins with the local level model, explaining filtering, smoothing, and forecasting techniques, including the Kalman filter, regression lemma, and Bayesian treatment. It then moves on to linear state space models, discussing univariate and multivariate structural time series models, ARMA and ARIMA models, exponential smoothing, regression models, and dynamic factor models. The text also explores continuous-time state space models, spline smoothing, and further comments on state space analysis, comparing it with Box-Jenkins approaches and benchmarking. The second part of the book focuses on non-Gaussian and non-linear state space models, covering special cases, heavy-tailed distributions, stochastic volatility models, and other financial models. It discusses approximate filtering and smoothing techniques, including the extended Kalman filter, unscented Kalman filter, and nonlinear smoothing. The book also introduces importance sampling for smoothing, particle filtering, and Bayesian estimation of parameters. It includes practical illustrations, such as the Nile data, and provides examples of non-Gaussian and nonlinear models, including Poisson, binary, and heavy-tailed densities. The book concludes with references, author index, and subject index, making it a valuable resource for researchers and practitioners in time series analysis.