Elements of Multivariate Time Series Analysis.

TLDR

Multivariate time series data arise in business, economics, engineering, geophysics, agriculture, and many other fields. The book aims to provide a comprehensive account of the basic concepts and methods for analyzing multivariate time series. It is self‑contained and covers topics from autocovariance matrices and vector ARMA models to forecasting, estimation, likelihood testing, and advanced subjects such as reduced‑rank structure, scalar component models, canonical correlation, unit‑root and co‑integration, and state‑space/Kalman filtering.

Abstract

This study is devoted to the analysis of multivariate time series data. Such data might arise in business and economics, engineering, geophysical sciences, agriculture, and many other fields. The emphasis is on providing an account of the basic concepts and methods which are useful in analyzing such data. The book presupposes a familiarity with univariate time series as might be gained from one term of a graduate course, but it is otherwise self-contained. It covers the basic topics such as autocovariance matrices of stationary processes, vector ARMA models and their properties, forecasting ARMA processes, least squares and maximum likelihood estimation techniques for vector AR and ARMA models, and associated likelihood ratio testing procedures for model building. In addition, it presents more advanced topics and techniques including reduced rank structure, structural indices, scalar component models, canonical correlation analyses for vector time series, multivariate nonstationary unit root models and co-integration structure, and state-space models and Kalman flltering techniques.