Time series models

Table of Contents: 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 11. ARCH and GARCH Models

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. This book presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. It 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. 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.