Forecasting VARMA processes using VAR models and subspace-based state space models
AbstractVAR modelling is a frequent technique in econometrics for linear processes. VAR modelling offers some desirable features such as relatively simple procedures for model specification (order selection) and the possibility of obtaining quick non-iterative maximum likelihood estimates of the system parameters. However, if the process under study follows a finite-order VARMA structure, it cannot be equivalently represented by any finite-order VAR model. On the other hand, a finite-order state space model can represent a finite-order VARMA process exactly, and, for state-space modelling, subspace algorithms allow for quick and non-iterative estimates of the system parameters, as well as for simple specification procedures. Given the previous facts, we check in this paper whether subspace-based state space models provide better forecasts than VAR models when working with VARMA data generating processes. In a simulation study we generate samples from different VARMA data generating processes, obtain VAR-based and state-space-based models for each generating process and compare the predictive power of the obtained models. Different specification and estimation algorithms are considered; in particular, within the subspace family, the CCA (Canonical Correlation Analysis) algorithm is the selected option to obtain state-space models. Our results indicate that when the MA parameter of an ARMA process is close to 1, the CCA state space models are likely to provide better forecasts than the AR models. We also conduct a practical comparison (for two cointegrated economic time series) of the predictive power of Johansen restricted-VAR (VEC) models with the predictive power of state space models obtained by the CCA subspace algorithm, including a density forecasting analysis.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 4235.
Date of creation: Oct 2006
Date of revision:
subspace algorithms; VAR; forecasting; cointegration; Johansen; CCA;
Find related papers by JEL classification:
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-08-08 (All new papers)
- NEP-ECM-2007-08-08 (Econometrics)
- NEP-ETS-2007-08-08 (Econometric Time Series)
- NEP-FOR-2007-08-08 (Forecasting)
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- Martin Wagner, 2002.
"A Comparison of Johansen's, Bierens and the Subspace Algorithm Method for Cointegration Analysis,"
dp0210, Universitaet Bern, Departement Volkswirtschaft.
- Martin Wagner, 2004. "A Comparison of Johansen's, Bierens' and the Subspace Algorithm Method for Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 399-424, 07.
- Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(01), pages 1-27, March.
- Takane, Yoshio & Yanai, Haruo & Hwang, Heungsun, 2006. "An improved method for generalized constrained canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 221-241, January.
- McCullough, B.D. & Wilson, Berry, 2005. "On the accuracy of statistical procedures in Microsoft Excel 2003," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1244-1252, June.
- Dietmar Bauer, 2005. "Comparing the CCA Subspace Method to Pseudo Maximum Likelihood Methods in the case of No Exogenous Inputs," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 631-668, 09.
- Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
- Bengtsson, Thomas & Cavanaugh, Joseph E., 2006. "An improved Akaike information criterion for state-space model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2635-2654, June.
- Godolphin, E.J. & Triantafyllopoulos, Kostas, 2006. "Decomposition of time series models in state-space form," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2232-2246, May.
- Diebold, Francis X & Mariano, Roberto S, 2002.
"Comparing Predictive Accuracy,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 134-44, January.
- Knusel, Leo, 2005. "On the accuracy of statistical distributions in Microsoft Excel 2003," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 445-449, March.
- Pollock, D. S. G., 2003. "Recursive estimation in econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 37-75, October.
- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
- Dietmar Bauer & Martin Wagner, 2000.
"Estimating Cointegrated Systems Using Subspace Algorithms,"
Econometric Society World Congress 2000 Contributed Papers
0293, Econometric Society.
- Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
- Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
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