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Backward and forward closed solutions of multivariate models


  • Ludlow, Jorge


Economic models that incorporate expectations require non causal time series theory. We provide a general method useful to solve in closed form any forward linear rational expectations multivariate model. An anticipative VARMA model is likely to explain a behavioral relation were a tentative future guides the today action. The work develops general conditions to get the unique stationary closed solution, backward or forward, so extends over the well known accepted results on causal invertible multivariate models and shows that to incorporate non causal models one should rely on Complex Analysis.

Suggested Citation

  • Ludlow, Jorge, 2010. "Backward and forward closed solutions of multivariate models," MPRA Paper 24139, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:24139

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    References listed on IDEAS

    1. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
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    More about this item


    Anticipative Times Series; anticipative VARMA; anticipative model; backward looking; forward looking; linear processes; linear filter; non casual model.;

    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

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