Consistency, distributional convergence, and optimality of score-driven filters

Eric A. Beutner, Yicong Lin and Andre Lucas
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Eric A. Beutner: Vrije Universiteit Amsterdam

No 23-051/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We study the in-fill asymptotics of score-driven time series models. For general forms of model mis-specification, we show that score-driven filters are consistent for the Kullback-Leibler (KL) optimal time-varying parameter path, which minimizes the pointwise KL divergence between the statistical model and the unknown dynamic data generating process. This directly implies that for a correctly specified predictive conditional density, score-driven filters consistently estimate the time-varying parameter path even if the model is mis-specified in other respects. We also obtain distributional convergence results for the filtering errors and derive the filter that minimizes the asymptotic filter error variance. Score-driven filters turn out to be optimal under correct specification of the predictive conditional density. The results considerably generalize earlier findings on the continuous-time consistency of volatility filters under mis-specification: they apply to biased filters, use weaker assumptions, allow for more general forms of mis-specification, and consider general time-varying parameters in non-linear time series models beyond the volatility case. Several examples are used to illustrate the theory, including time-varying tail shape models, dynamic copulas, and time-varying regression models.

Keywords: score-driven models; information theoretic optimality; Kullback-Leibler divergence; pseudo true time-varying parameters; in-fill asymptotics. (search for similar items in EconPapers)
JEL-codes: C22 C32 (search for similar items in EconPapers)
Date: 2023-08-30
New Economics Papers: this item is included in nep-ecm and nep-ets
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