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Vector Autoregresive Moving Average Identification for Macroeconomic Modeling: Algorithms and Theory

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  • D.S. Poskitt

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Abstract

This paper develops a new methodology for identifying the structure of VARMA time series models. The analysis proceeds by examining the echelon canonical form and presents a fully automatic data driven approach to model specification using a new technique to determine the Kronecker invariants. A novel feature of the inferential procedures developed here is that they work in terms of a canonical scalar ARMAX representation in which the exogenous regressors are given by predetermined contemporaneous and lagged values of other variables in the VARMA system. This feature facilitates the construction of algorithms which, from the perspective of macroeconomic modeling, are efficacious in that they do not use AR approximations at any stage. Algorithms that are applicable to both asymptotically stationary and unit-root, partially nonstationary (cointegrated) time series models are presented. A sequence of lemmas and theorems show that the algorithms are based on calculations that yield strongly consistent estimates.

Suggested Citation

  • D.S. Poskitt, 2009. "Vector Autoregresive Moving Average Identification for Macroeconomic Modeling: Algorithms and Theory," Monash Econometrics and Business Statistics Working Papers 12/09, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2009-12
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2009/wp12-09.pdf
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    References listed on IDEAS

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    1. Ravenna, Federico, 2007. "Vector autoregressions and reduced form representations of DSGE models," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2048-2064, October.
    2. Poskitt, D.S., 2006. "On The Identification And Estimation Of Nonstationary And Cointegrated Armax Systems," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1138-1175, December.
    3. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    4. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    5. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, May.
    6. George Athanasopoulos & D.S. Poskitt & Farshid Vahid, 2007. "Two canonical VARMA forms: Scalar component models vis-à-vis the Echelon form," Monash Econometrics and Business Statistics Working Papers 10/07, Monash University, Department of Econometrics and Business Statistics, revised May 2009.
    7. Cooley, Thomas F. & Dwyer, Mark, 1998. "Business cycle analysis without much theory A look at structural VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 57-88.
    8. Poskitt, D. S., 2003. "On the specification of cointegrated autoregressive moving-average forecasting systems," International Journal of Forecasting, Elsevier, vol. 19(3), pages 503-519.
    9. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    10. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    11. Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
    12. Wallis, Kenneth F, 1977. "Multiple Time Series Analysis and the Final Form of Econometric Models," Econometrica, Econometric Society, vol. 45(6), pages 1481-1497, September.
    13. D. S. Poskitt, 2005. "A Note on the Specification and Estimation of ARMAX Systems," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 157-183, March.
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    Cited by:

    1. Christian Kascha & Carsten Trenkler, 2011. "Cointegrated VARMA models and forecasting US interest rates," ECON - Working Papers 033, Department of Economics - University of Zurich.

    More about this item

    Keywords

    Keywords: Algorithms; asymptotically stationary and cointegrated time series; echelon;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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