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Andre LUCAS (VU Amsterdam) “Consistency, distributional convergence, and optimality of score-driven filters

April 4 @ 10:00 am - 11:00 pm

Finance & Financial Econometrics : 
Time: 10.00 am
Date: 04th of April 2024
Room 3001

Andre LUCAS (VU Amsterdam) “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.

Joint work: E. Beutner and Y. Lin