Izquierdo, Segismundo S. and Hernández, Cesáreo and del Hoyo, Juan (2006): Forecasting VARMA processes using VAR models and subspacebased state space models.

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Abstract
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 noniterative maximum likelihood estimates of the system parameters. However, if the process under study follows a finiteorder VARMA structure, it cannot be equivalently represented by any finiteorder VAR model. On the other hand, a finiteorder state space model can represent a finiteorder VARMA process exactly, and, for statespace modelling, subspace algorithms allow for quick and noniterative estimates of the system parameters, as well as for simple specification procedures.
Given the previous facts, we check in this paper whether subspacebased 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 VARbased and statespacebased 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 statespace 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 restrictedVAR (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 subspacebased state space models 
Language:  English 
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 
Item ID:  4235 
Depositing User:  Segismundo Izquierdo 
Date Deposited:  24. Jul 2007 
Last Modified:  09. Mar 2015 10:06 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/4235 