Multiple Time Series Models Applied To Panel Data

Many analyses of time series data involve multiple, related variables. Modeling Multiple Time Series presents many specification choices and special challenges. This book reviews the main competing approaches to modeling multiple time series: simultaneous equations, ARIMA, error correction models, and vector autoregression. The text focuses on vector autoregression (VAR) models as a generalization of the other approaches mentioned. Specification, estimation, and inference using these models is discussed. The authors also review arguments for and against using multi-equation time series models. Two complete, worked examples show how VAR models can be employed. An appendix discusses software that can be used for multiple time series models and software code for replicating the examples is available. Key Features: * Offers a detailed comparison of different time series methods and approaches. * Includes a self-contained introduction to vector autoregression modeling. * Situates multiple time series modeling as a natural extension of commonly taught statistical models.

Abstract: This study presents a general methodology for fitting multiple time series models to panel data. The basic statistical framework considered here consists of a dynamic simultaneous equation model where disturbances follow a permanent-transitory scheme with transitory components generated by a multivariate autoregressive-moving average process. This error scheme admits a wide variety of autocovariance patterns and provides a flexible framework for describing the dynamic characteristics of longitudinal data with a minimal number of parameters. It is possible within this framework to consider generally specified rational distributed lag structures involving both exogenous and endogenous variables which includes infinite order lag relationships. This paper outlines the generalizations of standard time series models that are possible when using panel data, and it identifies those instances in which procedures found in the time series literature cannot be directly applied to analyze longitudinal data. Data analysis techniques in the tine series literature are adapted for panel data analysis. These techniques aid in the choice of a time series model and prevent one from choosing a specification that is broadly inconsistent with the data. Several estimation procedures are proposed that can be used to estimate all the parameters of a multiple tine series model including both regression coefficients and parameters of the covariance matrix. The techniques developed here are robust in the sense that they do not rely on any specific distributional assumptions for their asymptotic properties, and in many cases their implementation requires only standard computer packages.

This book presents modern developments in time series econometrics that are applied to macroeconomic and financial time series, bridging the gap between methods and realistic applications. It presents the most important approaches to the analysis of time series, which may be stationary or nonstationary. Modelling and forecasting univariate time series is the starting point. For multiple stationary time series, Granger causality tests and vector autogressive models are presented. As the modelling of nonstationary uni- or multivariate time series is most important for real applied work, unit root and cointegration analysis as well as vector error correction models are a central topic. Tools for analysing nonstationary data are then transferred to the panel framework. Modelling the (multivariate) volatility of financial time series with autogressive conditional heteroskedastic models is also treated.

This study presents a general methodology for fitting multiple time series models to panel data. The basic statistical framework considered here consists of a dynamic simultaneous equation model where disturbances follow a permanent-transitory scheme with transitory components generated by a multivariate autoregressive-moving average process. This error scheme admits a wide variety of autocovariance patterns and provides a flexible framework for describing the dynamic characteristics of longitudinal data with a minimal number of parameters. It is possible within this framework to consider generally specified rational distributed lag structures involving both exogenous and endogenous variables which includes infinite order lag relationships. This paper outlines the generalizations of standard time series models that are possible when using panel data, and it identifies those instances in which procedures found in the time series literature cannot be directly applied to analyze longitudinal data. Data analysis techniques in the tine series literature are adapted for panel data analysis. These techniques aid in the choice of a time series model and prevent one from choosing a specification that is broadly inconsistent with the data. Several estimation procedures are proposed that can be used to estimate all the parameters of a multiple tine series model including both regression coefficients and parameters of the covariance matrix. The techniques developed here are robust in the sense that they do not rely on any specific distributional assumptions for their asymptotic properties, and in many cases their implementation requires only standard computer packages

R is a language and environment for data analysis and graphics. It may be considered an implementation of S, an award-winning language initially - veloped at Bell Laboratories since the late 1970s. The R project was initiated by Robert Gentleman and Ross Ihaka at the University of Auckland, New Zealand, in the early 1990s, and has been developed by an international team since mid-1997. Historically, econometricians have favored other computing environments, some of which have fallen by the wayside, and also a variety of packages with canned routines. We believe that R has great potential in econometrics, both for research and for teaching. There are at least three reasons for this: (1) R is mostly platform independent and runs on Microsoft Windows, the Mac family of operating systems, and various ?avors of Unix/Linux, and also on some more exotic platforms. (2) R is free software that can be downloaded and installed at no cost from a family of mirror sites around the globe, the Comprehensive R Archive Network (CRAN); hence students can easily install it on their own machines. (3) R is open-source software, so that the full source code is available and can be inspected to understand what it really does, learn from it, and modify and extend it. We also like to think that platform independence and the open-source philosophy make R an ideal environment for reproducible econometric research.

Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.

This book presents the numerous tools for the econometric analysis of time series. The text is designed with emphasis on the practical application of theoretical tools. Accordingly, material is presented in a way that is easy to understand. In many cases intuitive explanation and understanding of the studied phenomena are offerd. Essential concepts are illustrated by clear-cut examples. The attention of readers is drawn to numerous applied works where the use of specific techniques is best illustrated. Such applications are chiefly connected with issues of recent economic transition and European integration. The outlined style of presentation makes the book also a rich source of references. The text is divided into five major sections. The first section, “The Nature of Time Series”, gives an introduction to time series analysis. The second section, “Difference Equations”, describes briefly the theory of difference equations with an emphasis on results that are important for time series econometrics. The third section, “Univariate Time Series”, presents the methods commonly used in univariate time series analysis, the analysis of time series of one single variable. The fourth section, “Multiple Time Series”, deals with time series models of multiple interrelated variables. The fifth section “Panel Data and Unit Root Tests”, deals with methods known as panel unit root tests that are relevant to issues of convergence. Appendices contain an introduction to simulation techniques and statistical tables. Kniha přináší soubor základních i pokročilých technik a postupů používaných v ekonometrické analýze časových řad. Kniha klade důraz na umožnění efektivního použití popsaných technik v aplikovaném ekonomickém výzkumu. Toho je dosaženo tím, že teoretické základy popsané ekonometrie jsou prezentovány spolu s intuitivním vysvětlením problematiky a jednotlivé techniky jsou ilustrovány na výsledcích současného výzkumu a to především v kontextu procesu nedávné ekonomické transformace a současné evropské integrace. Toto pojetí z knihy činí nejen učebnici v klasickém smyslu, ale také užitečný referenční zdroj neboť odkazy v knize spojují klasickou i moderní ekonometrickou literaturu se soudobými aplikacemi, na nichž je použití jednotlivých technik jasně pochopitelné. Mnohá použití vycházejí z bohaté předchozí práce autorů v oboru. Text knihy je rozdělen do pěti hlavních částí. První část, “The Nature of Time Series”, přináší úvod do analýzy časových řad a popis jejich nejdůležitějších charakteristik, vlastností a procesů. Druhá část, “Difference Equations”, stručně popisuje teorii diferenciálních rovnic s důrazem na aspekty, které jsou klíčové v ekonometrii časových řad. Třetí část, “Univariate Time Series”, poměrně rozsáhle popisuje techniky, které se používají při analýze jednotlivých časových řad bez jejich vzájemené interakce a zahrnuje jak lineární tak nelineární modelované struktury. Čtvrtá část, “Multiple Time Series”, popisuje modely které umožňují analýzu několika časových řad a jejich vzájemných interakcí. Pátá část “Panel Data and Unit Root Tests”, zahrnuje některé techniky postavené na panelových datech, jež k průřezovým datům přidávají časovou dimenzi a vztahují se k analýze konvergence. Závěr knihy je doplněn o úvod do simulační techniky a statistické tabulky

The book describes and illustrates many advances that have taken place in a number of areas in theoretical and applied econometrics over the past four decades.

Forecasting and multiple regression analysis; Forecasting time series described by trend and irregular components; Forecasting seasonal time series; The box-jenkins methodology.

This book is concerned with recent developments in time series and panel data techniques for the analysis of macroeconomic and financial data. It provides a rigorous, nevertheless user-friendly, account of the time series techniques dealing with univariate and multivariate time series models, as well as panel data models. It is distinct from other time series texts in the sense that it also covers panel data models and attempts at a more coherent integration of time series, multivariate analysis, and panel data models. It builds on the author's extensive research in the areas of time series and panel data analysis and covers a wide variety of topics in one volume. Different parts of the book can be used as teaching material for a variety of courses in econometrics. It can also be used as reference manual. It begins with an overview of basic econometric and statistical techniques, and provides an account of stochastic processes, univariate and multivariate time series, tests for unit roots, cointegration, impulse response analysis, autoregressive conditional heteroskedasticity models, simultaneous equation models, vector autoregressions, causality, forecasting, multivariate volatility models, panel data models, aggregation and global vector autoregressive models (GVAR). The techniques are illustrated using Microfit 5 (Pesaran and Pesaran, 2009, OUP) with applications to real output, inflation, interest rates, exchange rates, and stock prices.