Matrices are used in many fields such as statistics, econometrics, mathematics, natural sciences and engineering. They provide a concise, simple method for describing long and complicated computations. This is a comprehensive handbook and dictionary of terms for matrix theory.
This study is concerned with forecasting time series variables and the impact of the level of aggregation on the efficiency of the forecasts. Since temporally and contemporaneously disaggregated data at various levels have become available for many countries, regions, and variables during the last decades the question which data and procedures to use for prediction has become increasingly important in recent years. This study aims at pointing out some of the problems involved and at pro viding some suggestions how to proceed in particular situations. Many of the results have been circulated as working papers, some have been published as journal articles, and some have been presented at conferences and in seminars. I express my gratitude to all those who have commented on parts of this study. They are too numerous to be listed here and many of them are anonymous referees and are therefore unknown to me. Some early results related to the present study are contained in my monograph "Prognose aggregierter Zeitreihen" (Lutkepohl (1986a)) which was essentially completed in 1983. The present study contains major extensions of that research and also summarizes the earlier results to the extent they are of interest in the context of this study.
This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series. The models covered include vector autoregressive, cointegrated,vector autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models. Least squares, maximum likelihood and Bayesian methods are considered for estimating these models. Different procedures for model selection and model specification are treated and a wide range of tests and criteria for model checking are introduced. Causality analysis, impulse response analysis and innovation accounting are presented as tools for structural analysis. The book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their tasks. It bridges the gap to the difficult technical literature on the topic.
This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series. The models covered include vector autoregressive, cointegrated,vector autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models. Least squares, maximum likelihood and Bayesian methods are considered for estimating these models. Different procedures for model selection and model specification are treated and a wide range of tests and criteria for model checking are introduced. Causality analysis, impulse response analysis and innovation accounting are presented as tools for structural analysis. The book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their tasks. It bridges the gap to the difficult technical literature on the topic.
This graduate level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated, and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts is considered and impulse response analysis, dynamic multipliers as well as innovation accounting are presented as tools for structural analysis within the multiple time series context. This book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on this book. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their task. It enables the reader to perform his or her analyses in a gap to the difficult technical literature on the topic.
