Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/282864 
Year of Publication: 
2023
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2023-051/III
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
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.
Subjects: 
score-driven models
information theoretic optimality
Kullback-Leibler divergence
pseudo true time-varying parameters
in-fill asymptotics
JEL: 
C22
C32
Document Type: 
Working Paper

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