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Two canonical VARMA forms: Scalar component models vis-à-vis the Echelon form

  • George Athanasopoulos

    ()

  • D.S. Poskitt

    ()

  • Farshid Vahid

In this paper we study two methodologies which identify and specify canonical form VARMA models. The two methodologies are: (i) an extension of the scalar component methodology which specifies canonical VARMA models by identifying scalar components through canonical correlations analysis and (ii) the Echelon form methodology which specifies canonical VARMA models through the estimation of Kronecker indices. We compare the actual forms and the methodologies on three levels. Firstly we present a theoretical comparison. Secondly, we present a Monte-Carlo simulation study that compares the performance of the two methodologies in identifying some pre-specified data generating processes. Lastly we compare the out-of-sample forecast performance of the two forms when models are fitted to real macroeconomic data.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 10/07.

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Length: 25 pages
Date of creation: Jul 2007
Date of revision: May 2009
Handle: RePEc:msh:ebswps:2007-10
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  1. George Athanasopoulos & Farshid Vahid, 2008. "A complete VARMA modelling methodology based on scalar components," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 533-554, 05.
  2. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
  3. Víctor Gómez & Agustín Maravall, 1998. "Automatic Modeling Methods for Univariate Series," Banco de Espa�a Working Papers 9808, Banco de Espa�a.
  4. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
  5. Melard, G. & Pasteels, J. -M., 2000. "Automatic ARIMA modeling including interventions, using time series expert software," International Journal of Forecasting, Elsevier, vol. 16(4), pages 497-508.
  6. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
  7. Tsay, Ruey S, 1989. "Parsimonious Parameterization of Vector Autoregressive Moving Average Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 327-41, July.
  8. George Athanasopoulos & Farshid Vahid, 2006. "VARMA versus VAR for Macroeconomic Forecasting," Monash Econometrics and Business Statistics Working Papers 4/06, Monash University, Department of Econometrics and Business Statistics.
  9. Nsiri, Saïd & Roy, Roch, 1996. "Identification of Refined ARMA Echelon Form Models for Multivariate Time Series," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 207-231, February.
  10. Clements, M.P. & Hendry, D., 1992. "On the Limitations of Comparing Mean Square Forecast Errors," Economics Series Working Papers 99138, University of Oxford, Department of Economics.
  11. Deistler, M. & Hannan, E. J., 1981. "Some properties of the parameterization of ARMA systems with unknown order," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 474-484, December.
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