APPLIED TIME SERIES ECONOMETRICS

APPLIED TIME SERIES ECONOMETRICS Edited by HELMUT LÜTKEPOHL European University Institute, Florence MARKUS KRÄTZIG Humboldt University, Berlin

CAMBRIDGE UNIVERSITY PRESS

Contents

Preface Notation and Abbreviations List of Contributors 1 Initial Tasks and Overview Helmut Lütkepohl 1.1 Introduction 1.2 Setting Up an Econometric Project 1.3 Getting Data 1.4 Data Handling 1.5 Outline of Chapters 2 Univariate Time Series Analysis Helmut Lütkepohl 2.1 Characteristics of Time Series 2.2 Stationary and Integrated Stochastic Processes 2.2.1 Stationarity 2.2.2 Sample Autocorrelations, Partial Autocorrelations, and Spectral Densities 2.2.3 Data Transformations and Filters 2.3 Some Popular Time Series Models 2.3.1 Autoregressive Processes 2.3.2 Finite-Order Moving Average Processes 2.3.3 AR1MA Processes 2.3.4 Autoregressive Conditional Heteroskedasticity 2.3.5 Deterministic Terms 2.4 Parameter Estimation 2.4.1 Estimation of AR Models 2.4.2 Estimation of ARM A Models 2.5 Model Specification

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Contents

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2.6

2.7

2.8 2.9

2.10

2.5.1 AR Order Specification Criteria 2.5.2 Specifying More General Models Model Checking 2.6.1 Descriptive Analysis of the Residuals 2.6.2 Diagnostic Tests of the Residuals 2.6.3 Stability Analysis Unit Root Tests 2.7.1 Augmented Dickey-Fuller (ADF) Tests 2.7.2 Schmidt-Phillips Tests 2.7.3 A Test for Processes with Level Shift 2.7.4 KPSSTest 2.7.5 Testing for Seasonal Unit Roots Forecasting Univariate Time Series Examples 2.9.1 German Consumption 2.9.2 Polish Productivity Where to Go from Here

3 Vector Autoregressive and Vector Error Correction Models Helmut Liitkepohl 3.1 Introduction 3.2 VARsandVECMs 3.2.1 The Models 3.2.2 Deterministic Terms 3.2.3 Exogenous Variables 3.3 Estimation 3.3.1 Estimation of an Unrestricted VAR 3.3.2 Estimation of VECMs 3.3.3 Restricting the Error Correction Term 3.3.4 Estimation of Models with More General Restrictions and Structural Forms 3.4 Model Specification 3.4.1 Determining the Autoregressive Order 3.4.2 Specifying the Cointegrating Rank 3.4.3 Choice of Deterministic Term 3.4.4 Testing Restrictions Related to the Cointegration Vectors and the Loading Matrix 3.4.5 Testing Restrictions for the Short-Run Parameters and Fitting Subset Models 3.5 Model Checking 3.5.1 Descriptive Analysis of the Residuals 3.5.2 Diagnostic Tests 3.5.3 Stability Analysis

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Contents 3.6 Forecasting VAR Processes and VECMs 3.6.1 Known Processes 3.6.2 Estimated Processes 3.7 Granger-Causality Analysis 3.7.1 The Concept 3.7.2 Testing for Granger-Causality 3.8 An Example 3.9 Extensions 4 Structural Vector Autoregressive Modeling and Impulse Responses Jörg Breitung, Ralf Brüggemann, and Helmut Lütkepohl 4.1 Introduction 4.2 The Models 4.3 Impulse Response Analysis 4.3.1 Stationary VAR Processes 4.3.2 Impulse Response Analysis of Nonstationary VARs and VECMs 4.4 Estimation of Structural Parameters 4.4.1 SVAR Models 4.4.2 Structural VECMs 4.5 Statistical Inference for Impulse Responses 4.5.1 Asymptotic Estimation Theory 4.5.2 Bootstrapping Impulse Responses 4.5.3 An Illustration 4.6 Forecast Error Variance Decomposition 4.7 Examples 4.7.1 A Simple AB-Model 4.7.2 The Blanchard-Quah Model 4.7.3 An SVECM for Canadian Labor Market Data 4.8 Conclusions 5 Conditional Heteroskedasticity Helmut Herwartz 5.1 Stylized Facts of Empirical Price Processes 5.2 Univariate GARCH Models 5.2.1 Basic Features of GARCH Processes 5.2.2 Estimation of GARCH Processes 5.2.3 Extensions 5.2.4 Blockdiagonality of the Information Matrix 5.2.5 Specification Testing 5.2.6 An Empirical Illustration with Exchange Rates 5.3 Multivariate GARCH Models

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Contents 5.3.1 5.3.2 5.3.3 5.3.4

Alternative Model Specifications Estimation of Multivariate GARCH Models Extensions Continuing the Empirical Illustration

6 Smooth Transition Regression Modeling Timo Teräsvirta 6.1 Introduction 6.2 The Model 6.3 The Modeling Cycle 6.3.1 Specification 6.3.2 Estimation of Parameters 6.3.3 Evaluation 6.4 Two Empirical Examples 6.4.1 Chemical Data 6.4.2 Demand for Money (Ml) in Germany 6.5 Final Remarks 7 Nonparametric Time Series Modeling Rolf Tschernig 7.1 Introduction 7.2 Local Linear Estimation 7.2.1 The Estimators 7.2.2 Asymptotic Properties 7.2.3 Confidence Intervals 7.2.4 Plotting the Estimated Function 7.2.5 Forecasting 7.3 Bandwidth and Lag Selection 7.3.1 Bandwidth Estimation 7.3.2 Lag Selection 7.3.3 Illustration 7.4 Diagnostics 7.5 Modeling the Conditional Volatility 7.5.1 Estimation 7.5.2 Bandwidth Choice 7.5.3 Lag Selection 7.5.4 ARCH Errors 7.6 Local Linear Seasonal Modeling 7.6.1 The Seasonal Nonlinear Autoregressive Model 7.6.2 The Seasonal Dummy Nonlinear Autoregressive Model 7.6.3 Seasonal Shift Nonlinear Autoregressive Model

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Contents 7.7 Example I: Average Weekly Working Hours in the United States 7.8 Example II: XETRA Dax Index The Software JMulTi Markus Krätzig 8.1 Introduction to JMulTi 8.1.1 Software Concept 8.1.2 Operating JMulTi 8.2 Numbers, Dates, and Variables in JMulTi 8.2.1 Numbers 8.2.2 Numbers in Tables 8.2.3 Dates 8.2.4 Variable Names 8.3 Handling Data Sets 8.3.1 Importing Data 8.3.2 Excel Format 8.3.3 ASCII Format 8.3.4 JMulTi .dat Format 8.4 Selecting, Transforming, and Creating Time Series 8.4.1 Time Series Selector 8.4.2 Time Series Calculator 8.5 Managing Variables in JMulTi 8.6 Notes for Econometric Software Developers 8.6.1 General Remark 8.6.2 T h e J S t a t C o m Framework 8.6.3 Component Structure 8.7 Conclusion References Index

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