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Backward and forward closed solutions of multivariate ARMA models

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  • Ludlow-Wiechers, Jorge

Abstract

Some of the most widely used models in economics are based on variables not yet observed, and their specification depends on future observations; the theory that underpins these delivers the backward/ forward solution. We present a newly unified construction, starting with a more general specification of an ARMA model, yet is capable of delivering in closed form, in both the backward and forward cases, leading to an alternative presentation of causal/non-causal and invertible/non-invertible cases.

Suggested Citation

  • Ludlow-Wiechers, Jorge, 2012. "Backward and forward closed solutions of multivariate ARMA models," MPRA Paper 37635, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37635
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    References listed on IDEAS

    as
    1. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, December.
    2. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Causal models; non-causal models; invertible models; non-invertible models; backward solution; forward solution;
    All these keywords.

    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
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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