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

Arbeitspapier

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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Tinbergen Institute Discussion Paper ; No. TI 2023-051/III

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
• Thema: score-driven models ; information theoretic optimality ; Kullback-Leibler divergence ; pseudo true time-varying parameters ; in-fill asymptotics

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Beutner, Eric A. ; Lin, Yicong ; Lucas, André
• Ereignis: Veröffentlichung
• (wer): Tinbergen Institute
• (wo): Amsterdam and Rotterdam
• (wann): 2023

Weitere Informationen

• Handle: http://hdl.handle.net/10419/282864
• Letzte Aktualisierung: 10.03.2025, 11:41 MEZ