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.
This article 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. In contrast to previous literature, the novel representation of the MA polynomial matrix using the Wiener-Hopf factorisation (WHF) focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models . 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 and analytic expressions for the score and the information matrix. As application, we estimate the Blanchard and Quah model and show that our method provides further insights regarding non-invertibility using a standard macroeconometric model. These and further analyses are implemented in a well documented R-package.
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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)
focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models
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. The estimation procedure is illustrated with various examples from the economic literature and implemented as
and analytic expressions for the score and the information matrix. As application, we estimate the Blanchard and Quah model and show that our method provides further insights regarding non-invertibility using a standard macroeconometric model. These and further analyses are implemented in a well documented