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This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.
List of contents
Preface.- 1 Time Series and Stationary Processes.- 2 Prediction.- 3 Spectral Representation.- 4 Filter.- 5 Autoregressive Processes.- 6 ARMA Systems and ARMA Processes.- 7 State-Space Systems.- 8 Models with Exogenous Variables.- 9 Granger Causality.- 10 Dynamic Factor Models.- 10 ARCH and GARCH Models.- Index.
About the author
Manfred Deistler is Emeritus Professor of Econometrics and System Theory at the Institute of Statistics and Mathematical Methods in Economics at the TU Wien, Vienna, Austria. His research interests include time series analysis, systems identification and econometrics. He is a Fellow of the Econometric Society, the IEEE, and the Journal of Econometrics.
Wolfgang Scherrer is a Professor of Econometrics and System Theory at the Institute of Statistics and Mathematical Methods in Economics at the TU Wien, Vienna, Austria. His research interests include time series analysis, econometrics, dynamic factor models and applications in the area of energy supply.
Report
"The book is not too long, with roughly 200 pages, which is advantageous for the use in lectures. ... it is also well suited for seminars following such lectures on more advanced topics in time series analysis. ... the book fills a small but important gap in the literature, finding its place in the plethora of time series textbooks." (Claudia Kirch, zbMATH 1532.62006, 2024)
"This lecture note is recommended as a textbook that is quite plainly written for graduate students and research workers who are interested in deeply understanding time series modeling." (Yuzo Hosoya, Mathematical Reviews, October, 2023)
