Izquierdo, Segismundo S. and Hernández, Cesáreo and del Hoyo, Juan (2006): Forecasting VARMA processes using VAR models and subspace-based state space models.
Download (3MB) | Preview
VAR 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.
|Item Type:||MPRA Paper|
|Institution:||University of Valladolid|
|Original Title:||Forecasting VARMA processes using VAR models and subspace-based state space models|
|Keywords:||subspace algorithms; VAR; forecasting; cointegration; Johansen; CCA|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods; Simulation Methods
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation
|Depositing User:||Segismundo Izquierdo|
|Date Deposited:||24. Jul 2007|
|Last Modified:||11. Feb 2013 16:55|
Aoki, M., 1990. State Space Modeling of Time Series. Second, Revised and Enlarged Edition. Springer-Verlag.
Aoki, M. and Havenner, A., 1991. State Space Modeling of Multiple Time Series. Economet. Rev. 10 (1), 1-59.
Bauer, D., 2005a. Asymptotic Properties of Subspace Estimators. Automatica 41 (3), 359-376.
Bauer, D., 2005b. Comparing the CCA Subspace Method to Pseudo Maximum Likelihood Methods in the case of No Exogenous Inputs. J. Time Series Analysis 26 (5), 631-668.
Bauer, D. and Ljung, L., 2002. Some Facts about the Choice of the Weighting Matrices in Larimore Type of Subspace Algorithms. Automatica 38 (5), 763-773.
Bauer, D. and Wagner, M., 2002. Estimating Cointegrated Systems using Subspace Algorithms. J. Econometrics 111, 47-84.
Bauer, D. and Wagner, M., 2003. The Performance of Subspace Algorithm Cointegration Analysis: A Simulation Study. Working paper, University of Bern.
Bengtsson, T. and Cavanaugh, J.E., 2006. An improved Akaike Information Criterion for State-space Model Selection. Comput. Stat. Data An. 50 (10), 2635-2654.
Brown, R. Durbin, J. and Evans, J., 1975. Techniques for Testing the Constancy of Regression Relationships over Time. J. Roy. Stat. Soc. B 37, 149-172.
Clements, M.P. and Smith, J., 2000. Evaluating the Forecast Densities of Linear and Non-linear Models: Applications to Output Growth and Unemployment. J. Forecasting 19, 255-276.
De Cock, K. and De Moor, B., 2003. Subspace Identification Methods, in Contribution to section 5.5, “Control systems robotics and automation” of EOLSS, UNESCO Encyclopedia of Life Support Systems, (Unbehauen H.D.), vol. 1 of 3, Eolss Publishers Co., Ltd. (Oxford, UK), 933-979.
Diebold, F.X., Günther T.A. and Tay, A.S., 1998. Evaluating Density Forecasts with Applications to Financial Risk Management. Int. Econ. Rev. 39 (4), 863-883.
Diebold, F.X., Hahn, J. and Tay, A.S., 1999. Multivariate Density Forecast Evaluation and Calibration in Financial Risk Management: High Frecuency Returns on Foreign Exchange. Rev. Econ. Stat. 81, 661-673.
Diebold, F.X. and Mariano, R.S., 2002. Comparing Predictive Accuracy. J. Bus. Econ. Stat. 20 (1), 134-44.
Godolphin, E.J. and Triantafyllopoulos, K., 2006. Decomposition of Time Teries Models in State-space Form. Comput. Stat. Data An. 50 (9), 2232-2246.
Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press.
Hannan, E. and Deistler, M., 1988. The Statistical Theory of Linear Systems. Wiley, New York.
Harvey, A.C., 1989. Forecasting, Structural Time Series and the Kalman Filter. Cambridge University Press.
Johansen, S., 1988. Statistical Analysis of Cointegration Vectors. J. Econ. Dyn. Control 12, 231-254.
Knusel, L., 2005. On the accuracy of statistical distributions in Microsoft Excel 2003. Comput. Stat. Data An. 48 (3), 445-449.
Kuha, J., 2004. AIC and BIC. Comparisons of Assumptions and Performance. Sociol. Method. Res. 33 (2), 188-229.
Larimore, W.E., 1983. System Identification, Reduced Order Filters and Modelling via Canonical Variate Analysis. In: Rao, H.S., Dorato, P. (Eds.), Proceedings of the 1983 American Control Conference, Vol. 2, IEEE Service Center, Piscataway, NJ, 445-451.
Larimore, W.E., 2000. Identification of Collinear and Cointegrated Multivariable Systems using Canonical Variate Analysis. IFAC SYSID’99.
Ljung, L., 1999. System Identification. Theory for the User. 2nd edition. Prentice Hall.
Ljung, L., 2006. System Identification Toolbox For Use with MATLAB®. User´s Guide. Version 6. The MathWorks.
Lütkepohl, H., 1991. Introduction to Multiple Time Series Analysis. Springer-Verlag.
McCullough,B.D., Wilson,B., 2005. On the accuracy of statistical procedures in Microsoft Excel 2003. Comput. Stat. Data An. 49 (4), 1244-1252.
Pollock, D.S.G., 1999. Time-Series Analysis, Signal Processing and Dynamics. Academic Press, London.
Pollock, D.S.G., 2003. Recursive Estimation in Econometrics. Comput. Stat. Data An. 44 (1-2), 37-75.
Reinsel, G.C. and Velu, R.P., 1998. Multivariate Reduced-Rank Regression, Theory and Applications. Springer-Verlag.
Saikkonen, P., 1992. Estimation and Testing of Cointegrated Systems by Autoregressive Approximation. Economet. Theor. 8, 1-27.
Siegel, S. and Castellan, N.J., 1988. Non Parametric Statistics for the Behavioural Sciences. 2nd edition. McGraw-Hill.
Stock, J.H. and Watson, M.W., 1988. Testing for Common Trends. J. Am. Stat. Assoc. 83, 1097-1107.
Takane, Y., Yanai, H. and Hwang, H., 2006. An improved method for generalized constrained canonical correlation analysis. Comput. Stat. Data An. 50 (1), 221-241.
Tay, A.S. and Wallis, K.F., 2000. Density Forecasting: A Survey. J. Forecasting 19, 235-254.
Terceiro, J., 1990. Estimation of Dynamic Econometric Models with Errors in variables. Berlin: Springer-Verlag.
Van Oberschee, P. and De Moor, B., 1996. Subspace Identification for Linear Systems: Theory – Implementation - Applications. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Viberg, M., 1995. Subspace-based Methods for the Identification of Linear Time-invariant Systems. Automatica 31 (12), 1835-1851.
Wagner, M., 1999. VAR Cointegration in VARMA Models. Economics Series 65. Institute for Advanced Studies, Vienna.
Wagner, M., 2004. A Comparison of Johansen's, Bierens' and the Subspace Algorithm Method for Cointegration Analysis. Oxford B. Econ. Stat. 66 (3), 399-424.
Yap, S.F. and Reinsel, G.C., 1995. Estimating and testing for unit roots in a partially nonstationary vector autoregressive moving average model. J. Am. Stat. Assoc. 90, 253-267.