VAR Modeling and Business Cycle Analysis: A Taxonomy of Errors
AbstractIn this article we investigate the theoretical behaviour of finite lag VAR(n) models fitted to time series that in truth come from an infinite order VAR(?) data generating mechanism. We show that overall error can be broken down into two basic components, an estimation error that stems from the difference between the parameter estimates and their population ensemble VAR(n) counterparts, and an approximation error that stems from the difference between the VAR(n) and the true VAR(?). The two sources of error are shown to be present in other performance indicators previously employed in the literature to characterize, so called, truncation effects. Our theoretical analysis indicates that the magnitude of the estimation error exceeds that of the approximation error, but experimental results based upon a prototypical real business cycle model indicate that in practice the approximation error approaches its asymptotic position far more slowly than does the estimation error, their relative orders of magnitude notwithstanding. The experimental results suggest that with sample sizes and lag lengths like those commonly employed in practice VAR(n) models are likely to exhibit serious errors of both types when attempting to replicate the dynamics of the true underlying process and that inferences based on VAR(n) models can be very untrustworthy.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 11/12.
Length: 22 pages
Date of creation: 19 Apr 2012
Date of revision:
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Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Find related papers by JEL classification:
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
- E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-02 (All new papers)
- NEP-ECM-2012-05-02 (Econometrics)
- NEP-ETS-2012-05-02 (Econometric Time Series)
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