Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation

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This paper deals with parameterisation, identifiability, and maximum likelihood (ML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. We introduce a new parameterisation of the MA polynomial matrix based on the Wiener-Hopf factorisation (WHF) and show that the model is identified in this parametrisation for a generic set in the parameter space (when certain just-identifying restrictions are imposed). When the SVARMA model is driven by Gaussian errors, neither the static shock transmission matrix, nor the location of the determinantal zeros of the MA polynomial matrix can be identified without imposing further identifying restrictions on the parameters. We characterise the classes of observational equivalence with respect to second moment information at different stages of the modelling process. Subsequently, cross-sectional and temporal independence and non-Gaussianity of the shocks is used to solve these identifiability problems and identify the true root location of the MA polynomial matrix as well as the static shock transmission matrix (up to permutation and scaling).Typically imposed identifying restrictions on the shock transmission matrix as well as on the determinantal root location are made testable. Furthermore, we provide low level conditions for asymptotic normality of the ML estimator. The estimation procedure is illustrated with various examples from the economic literature and implemented as R-package.
TidskriftJournal of Econometrics
StatusInsänt - 11 feb 2020
MoE-publikationstypA1 Tidskriftsartikel-refererad

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