Multivariate Techniques

Most of the observable phenomena in the empirical sciences are of multivariate nature. This book presents the tools and concepts of multivariate data analysis with a strong focus on applications. The text is devided into three parts. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents from a theoretical point of view distributions, estimators and tests for various practical situations. The last part covers multivariate techniques and introduces the reader into the wide basket of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises.

Wildlife researchers and ecologists make widespread use of multivariate statistics in their studies. With its focus on the practical application of the techniques of multivariate statistics, this book shapes the powerful tools of statistics for the specific needs of ecologists and makes statistics more applicable to their course of study.

The use of methods of time series analysis in the study of multivariate time series has become of increased interest in recent years. Although the methods are rather well developed and understood for univarjate time series analysis, the situation is not so complete for the multivariate case. This book is designed to introduce the basic concepts and methods that are useful in the analysis and modeling of multivariate time series, with illustrations of these basic ideas. The development includes both traditional topics such as autocovariance and auto­ correlation matrices of stationary processes, properties of vector ARMA models, forecasting ARMA processes, least squares and maximum likelihood estimation techniques for vector AR and ARMA models, and model checking diagnostics for residuals, as well as topics of more recent interest for vector ARMA models such as reduced rank structure, structural indices, scalar component models, canonical correlation analyses for vector time series, multivariate unit-root models and cointegration structure, and state-space models and Kalman filtering techniques and applications.