# Multiple Time Series Models, Issue 148

SAGE, 2007 - Mathematics - 99 pages
Many analyses of time series data involve multiple, related variables. Multiple Time Series Models 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 FeaturesOffers 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.

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This is very much a terse text on multiple time series. The one by Lutkepohl is comprehensive and detailed, but this one gives you a quick reference on the go. It's also a tribute to the co-author J.T. Williams.

### Contents

 Introduction to Multiple Time Series Models 1 11 Simultaneous Equation Approach 4 12 ARIMA Approach 6 13 Error Correction or LSE Approach 7 14 Vector Autoregression Approach 9 15 Comparison and Summary 12 Basic Vector Autoregression Models 14 21 Dynamic Structural Equation Models 15
 273 VAR Versus VECM ECM 54 28 Criticisms of VAR 56 Examples of VAR Analyses 59 311 Testing for Unit Roots 61 312 Specifying the Lag Length 62 313 Estimation of the VAR 63 314 Granger Causality Testing 65 315 Decomposition of the Forecast Error Variance 66

 22 Reduced Form Vector Autoregressions 18 23 Relationship of a Dynamic Structural Equation Model to a Vector Autoregression Model 20 24 Working With This Model 22 25 Specification and Analysis of VAR Models 23 251 Estimation of VAR 24 253 Testing Serial Correlation in the Residuals 28 254 Granger Causality 32 255 Interpreting Granger Causality 34 256 Testing Other Restrictions in a VAR Model 36 258 Error Bands for Impulse Responses 41 259 Innovation Accounting or Decomposition of Forecast Error Variance 45 26 Other Specification Issues 48 261 Should Differencing Be Used for Trending Data? 49 27 Unit Roots and Error Correction in VARs 50 272 Error Correction as a VAR Model 52
 316 Impulse Response Analysis 68 32 Effective Corporate Tax Rates 71 321 Data 72 322 Testing for Unit Roots 73 324 Granger Causality Testing 74 325 Impulse Response Analysis 77 326 Decomposition of the Forecast Error Variance 79 327 A Further Robustness Check 81 33 Conclusion 82 Software for Multiple Time Series Models 85 Notes 89 References 92 Index 96 About the Authors 99 Copyright