Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2023-08-30
Number: 23-051/III
Author-Name: Eric A. Beutner
Author-Workplace-Name: Vrije Universiteit Amsterdam
Author-Name: Yicong Lin
Author-Workplace-Name: Vrije Universiteit Amsterdam
Author-Name: Andre Lucas
Author-Workplace-Name: Vrije Universiteit Amsterdam
Title: Consistency, distributional 
convergence, and
optimality of score-driven filters
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.
Classification-JEL: C22, C32
Keywords: score-driven models, information theoretic optimality, Kullback-Leibler divergence,
pseudo true time-varying parameters, in-fill asymptotics.

File-URL: https://papers.tinbergen.nl/23051.pdf
File-Format: application/pdf
File-Size: 2.315.383 bytes
Handle: RePEc:tin:wpaper:20230051