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Forecasting VARMA processes: VAR models vs. subspace-based state space models


  • Segismundo Izquierdo

    () (University of Valladolid)

  • Cesareo Hernandez

    (University of Valladolid)

  • Juan del Hoyo

    (University of Valladolid)


VAR modelling is a frequent technique in econometrics for assumed linear processes. VAR modelling offers some desirable features such as relatively simple procedures for model specification and the possibility of making a quick and non-iterative maximum likelihood estimation 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 subspace algorithms allow for a simple specification and quick non-iterative estimates. Given the previous facts, we test in this paper whether subspace-based state space models can provide better forecasts than VAR models when working with VARMA data generating processes. In a simulation study we generate identification 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. 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

Suggested Citation

  • Segismundo Izquierdo & Cesareo Hernandez & Juan del Hoyo, 2006. "Forecasting VARMA processes: VAR models vs. subspace-based state space models," Computing in Economics and Finance 2006 271, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:271

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    More about this item


    Forecasting; time series; subspace models;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods


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