Recursive estimation and time-series analysis. An introduction
This book is an introductory tutorial text for undergraduate or master's students, intended to introduce the reader to aspects of the theory and practice of recursive estimation, including its use in time-series analysis. The book consists of two parts, as follows: Part 1: Recursive parameter estimation and Part 2: Recursive time-series analysis. Part 1 includes the following chapters. Chapter 2: Recursive estimation: A tutorial introduction, which provides an introduction to recursive analysis for the case of the mean of a stationary random variable. Chapter 3: Recursive estimation and stochastic approximation, which develops the deterministic, recursive least squares (RLS) for multiple parameters. Chapter 4: RLS regression analysis, which shows how it is possible to modify the deterministic algorithm so that it constitutes the recursive version of linear LS regression analysis. Chapter 5: Recursive estimation of time-variable parameters in regression models, shows how the recursive algorithms are in an ideal form for extension to the estimation of time-variable parameters. Part 2 includes the following chapters. Chapter 6: The time-series estimation problem, which considers the polynomial matrix description (PMD) models. Chapter 7: The instrumental variables (IV) method of time series analysis, and Chapter 8: Optimum IV methods of time-series model estimation, which describe a method based on IV. Chapter 9: Alternative recursive approaches to time-series analysis, where the prediction error minimization for PMD models, the extended Kalman filter approach and the maximum likelihood method are discussed. Chapter 10: Recursive estimation: A general tool in data analysis and stochastic model building, outlines how recursive estimation procedures can prove useful as general tools in data analysis and model building. The book also contains an epilogue and three appendices, besides Chapter 1, which presents LS recursive estimation, going back to the early works of Gauss, Plackett and Kalman.
scientific article; zbMATH DE number 3866428