Empirical Vector Autoregressive Modeling

ISBN-13: 9783540577072 / Angielski / Miękka / 1994 / 382 str.

Marius Ooms

Opis

1. 1 Integrating results The empirical study of macroeconomic time series is interesting. It is also difficult and not immediately rewarding. Many statistical and economic issues are involved. The main problems is that these issues are so interrelated that it does not seem sensible to address them one at a time. As soon as one sets about the making of a model of macroeconomic time series one has to choose which problems one will try to tackle oneself and which problems one will leave unresolved or to be solved by others. From a theoretic point of view it can be fruitful to concentrate oneself on only one problem. If one follows this strategy in empirical application one runs a serious risk of making a seemingly interesting model, that is just a corollary of some important mistake in the handling of other problems. Two well known examples of statistical artifacts are the finding of Kuznets "pseudo-waves" of about 20 years in economic activity (Sargent (1979, p. 248)) and the "spurious regression" of macroeconomic time series described in Granger and Newbold (1986, 6. 4). The easiest way to get away with possible mistakes is to admit they may be there in the first place, but that time constraints and unfamiliarity with the solution do not allow the researcher to do something about them. This can be a viable argument.

Spis treści

1 Introduction.- 1.1 Integrating results.- 1.2 Goal of the study.- 1.3 Data and measurement model.- 1.4 Baseline model and methodology.- 1.5 Outline of the study.- 1.6 What is new?.- 2 The Unrestricted VAR and its components.- 2.1 Introduction.- 2.2 The model.- 2.3 Univariate processes and unit roots.- 2.4 Integrated processes.- 2.4.1 Definitions and notation.- 2.4.2 MA representation, autocorrelation and pseudo spectrum.- 2.5 Alternative models for nonstationarity, long memory and persistence.- 2.5.1 Nonstationarity.- 2.5.2 Long memory, the variance time function and adjusted range analysis.- 2.5.3 Persistence.- Appendix A2.1 MA representation integrated process.- A2.1.1 MA representations.- A2.1.2 Pseudo autocorrelation functions.- Appendix A2.2 Univariate testing for unit root nonstationarity.- A2.2.1 The pure unit root case without deterministic terms.- A2.2.1.1 Notation and model.- A2.2.1.2 Discussion.- A2.2.2 Deterministic terms and unknown residual autocorrelation.- A2.2.2.1 Generalization of the test regression.- A2.2.2.2 Interesting null hypotheses, alternatives and tests.- A2.2.2.3 The parameters ?i and ?i in (A2.2.11) and (A2.2.12).- A2.2.2.4 Test statistics and distributions.- A2.2.2.5 Evaluation of methods.- A2.2.2.6 Other approaches and some extensions.- 3 Data Analysis by Vector Autoregression.- 3.1 Introduction.- 3.2 Data-oriented measures of influence.- 3.2.1 Goal of the influence analysis.- 3.2.2 Influence measures in regression.- 3.2.3 Influence measures for dynamic and multiple equation models.- 3.2.4 Other influence measures from multivariate analysis.- 3.3 Diagnostic checking.- 3.3.1 Choosing test statistics.- 3.3.2 Theoretical consideration for choosing tests.- 3.3.3 Practical considerations for choosing tests.- 3.3.4 Dynamic specification of the mean.- 3.3.5 Distribution of the disturbances.- 3.3.6 Parameter constancy of dynamic and covariance parameters.- 3.3.7 An alternative test for parameter stability.- 3.3.8 Multivariate diagnostics.- 3.3.9 A diagnostic for multivariate unit roots.- 3.3.10 Consequences of “rejection” of the model.- Appendix A3.1 Influence measures for the normal linear model.- A3.1.1 Global influence measures.- A3.1.2 Local influence measures.- Appendix A3.2 Influence measures for the multivariate general linear model.- Appendix A3.3 Influence measures in principal component analysis.- 4 Seasonality.- 4.1 Introduction.- 4.2 Application of the idea of unobserved components.- 4.3 Application of linear filters to estimate unobserved components.- 4.3.1 Optimal extraction in multivariate series.- 4.3.2 Optimal extraction in nonstationary series.- 4.3.3 Specification of low dimensional univariate models.- 4.3.4 Optimal extraction in a finite sample.- 4.3.5 Optimal extraction in the presence of outliers.- 4.4 Data analysis of the seasonal component.- 4.5 Application of the Census X-11 filter in a VAR.- Appendix 4.1 Trigonometric seasonal processes in regression.- A4.1.1 Notation and underlying model.- A4.1.2 Zero correlation between seasonal patterns.- A4.1.3 Circularity: Unit correlation between seasonal patterns.- Appendix 4.2 Backforecasts and deterministic changes in mean.- A4.2.1 Introduction.- A4.2.2 Backforecasting and deterministic changes in mean with linear trends.- A4.2.3 Backforecasting and deterministic changes in mean with seasonal dummies.- A4.2.4 Changes in mean in multivariate model with unit roots.- 5 Outliers.- 5.1 Introduction.- 5.2 The outlier model.- 5.3 Some effects of outliers on VAR estimates.- 5.3.1 Effect of outliers on unit root tests.- 5.3.2 Effect of outliers on estimates of ?.- 5.4 Derivation of the LM-statistics.- 5.4.1 Case of known parameters and timing.- 5.4.2 Case of estimated parameters and unknown timing.- 5.4.3 Distinguishing between outlier types.- 5.4.4 Distinguishing between outliers in different equations.- 5.5 An artificial example.- 5.6 Application to macroeconomic series.- 5.7 Two simple ways to study the influence of outliers.- Appendix 5.1 Some proofs concerning outlier test statistics.- A5.1.1 Derivation simultaneous test.- A5.1.2 Finite sample alternatives for I test procedure.- Appendix 5.2 Subsample analysis outlier influence.- Appendix 5.3 Robust estimation by extraction of additive outliers.- 6 Restrictions on the VAR.- 6.1 Introduction.- 6.2 Cointegration, the number of unit roots, and common trends.- 6.2.3 Vector error correction.- 6.2.4 Other parameterizations.- 6.3 Straightforward transformation formulae.- 6.3.1 From Campbell-Shiller to vector error correction.- 6.3.2 From vector error correction to Campbell-Shiller, mean growth.- 6.3.3 From vector error correction to common trends.- 6.3.4 Examples.- 6.3.5 Conditions for VECM, I(2)-ness, and explosive systems.- 6.4 Trend stationary processes and quadratic trends.- 6.5 Estimating pushing trends and pulling equilibria.- 6.5.1 Deterministic trends.- 6.5.2 Estimating the stochastic part of the trend.- 6.5.3 Estimating pulling equilibria.- 6.6 Multivariate tests for unit roots.- 6.6.1 Models with p = 1 and zero mean.- 6.6.2 Deterministic terms and serial correlation in AR(1) residuals.- Appendix 6.1 Computation and distribution multivariate unit root test statistics.- A6.1.1 Computation.- A6.1.2 Distribution.- 7 Applied VAR Analysis for Aggregate Investment.- 7.1 Introduction.- 7.2 The variable of interest and some of its supposed relationships.- 7.2.1 Theoretical relationships.- 7.2.2 Empirical models.- 7.3 Measurement model.- 7.3.1 Investment in the national accounts.- 7.3.2 Definition of investment.- 7.3.3 Other macroeconomic price indexes.- 7.4 Univariate analysis.- 7.4.1 The variables.- 7.4.2 Graphs and influence analysis.- 7.4.3 Representations of the autocorrelation function.- 7.4.4 Adjusted range techniques.- 7.4.6 Application.- 7.4.7 Results.- 7.4.7.1 Outliers.- 7.4.7.2 Autocorrelations.- 7.4.7.3 Long memory analysis.- 7.4.7.4 Data analysis seasonal components.- 7.4.7.5 Variance time functions.- 7.4.7.6 Statistical unit root analysis.- 7.4.7.7 Parameter stability.- 7.4.7.8 Summary of univariate results.- 7.5 Multivariate analysis.- 7.5.1 Predictions and seasonality in the unrestricted VAR.- 7.5.2 Unit root analysis.- 7.5.3 Detecting a structural break.- 7.5.4 The final model.- Appendix 7.1 Data sources and construction.- Appendix 7.2 Results of final VECM model.- Appendix 7.3 Open economy stochastic dynamic general equilibrium models.- Summary.- References.- Name index.