VARMAX and Transfer Function Models

  • Víctor Gómez
Part of the Statistics and Computing book series (SCO)


The vector random process {Yt} is said to follow a vector autoregressive moving average model with exogenous variables or VARMAX model if it satisfies an equation of the form.
$$\displaystyle \Phi (B) Y_{t} = \Omega (B) Z_{t} + \Theta (B) A_{t},$$
where B is the backshift operator, BYt = Yt−1, Φ(B) = I + Φ1B + ⋯ + ΦpBp, Ω(B) = Ω0 + Ω 1B + ⋯ + ΩrBr, Θ(B) = I + Θ 1B + ⋯ + ΘqBq, {Zt} is a process of strongly exogenous inputs with respect to {Yt}, and {At} is a multivariate white noise process. It is assumed that Zt and Av are orthogonal for all v ≤ t.


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Authors and Affiliations

  • Víctor Gómez
    • 1
  1. 1.General Directorate of BudgetsMinistry of Finance and Public AdministrationsMadridSpain

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