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

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Author Info
George Athanasopoulos ()
D.S. Poskitt ()
Farshid Vahid

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Abstract

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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File URL: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2007/wp10-07.pdf
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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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Related research
Keywords: Echelon form; Identification; Multivariate time series; Scalar component; VARMA model.;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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  1. 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. [Downloadable!] (restricted)
  2. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October. [Downloadable!] (restricted)
  3. 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.
  4. 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. [Downloadable!]
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  5. 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.
  6. George Athanasopoulos & Farshid Vahid, 2006. "A Complete VARMA Modelling Methodology Based on Scalar Components," Monash Econometrics and Business Statistics Working Papers 2/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
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