This paper investigates the focused information criterion and plug-in average for vector autoregressive models with local-to-zero misspeci cation. These methods have the advantage of focusing on a quantity of interest rather than aiming at overall model t. Any (su ciently regular) function of the parameters can be used as a quantity of interest. We determine the asymptotic properties and elaborate on the role of the locally misspeci ed parameters. In particular, we show that the inability to consistently estimate locally misspeci ed parameters translates into suboptimal selection and averaging. We apply this framework to impulse response analysis. A Monte Carlo simulation study supports our claims.

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