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

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Document pages: 29 pages

Abstract: This article deals with parameterisation, identifiability, and maximumlikelihood (ML) estimation of possibly non-invertible structural vectorautoregressive moving average (SVARMA) models driven by independent andnon-Gaussian shocks. In contrast to previous literature, the novelrepresentation of the MA polynomial matrix using the Wiener-Hopf factorisation(WHF) focuses on the multivariate nature of the model, generates insights intoits structure, and uses this structure for devising optimisation algorithms. Inparticular, it allows to parameterise the location of determinantal zerosinside and outside the unit circle, and it allows for MA zeros at zero, whichcan be interpreted as informational delays. This is highly relevant fordata-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models.Typically imposed identifying restrictions on the shock transmission matrix aswell as on the determinantal root location are made testable. Furthermore, weprovide low level conditions for asymptotic normality of the ML estimator andanalytic expressions for the score and the information matrix. As application,we estimate the Blanchard and Quah model and show that our method providesfurther insights regarding non-invertibility using a standard macroeconometricmodel. These and further analyses are implemented in a well documentedR-package.

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