Missing observations in observation-driven time series models

• Published in: Journal of econometrics Vol. 221; no. 2; pp. 542 - 568
• Main Authors: Blasques, F., Gorgi, P., Koopman, S.J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2021; Elsevier Science Publishers; Elsevier Sequoia S.A
• Subjects: Analysis; Asymptotic methods; Consistency; Estimating techniques; Inconsistency; Indirect inference; Inference; Measurement; Missing data; Monte Carlo method; Monte Carlo simulation; Observation-driven models; Simulation; Time series; Volatility; Missing data; C22; Indirect inference; Volatility; C58; Consistency; Observation-driven models
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2020.07.043

We argue that existing methods for the treatment of missing observations in time-varying parameter observation-driven models lead to inconsistent inference. We provide a formal proof of this inconsistency for a Gaussian model with time-varying mean. A Monte Carlo simulation study supports this theoretical result and illustrates how the inconsistency problem extends to score-driven and, more generally, to observation-driven models, which include well-known models for conditional volatility. To overcome the problem of inconsistent inference, we propose a novel estimation procedure based on indirect inference. This easy-to-implement method delivers consistent inference. The asymptotic properties of the new method are formally derived. Our proposed estimation procedure shows a promising performance in a Monte Carlo simulation exercise as well as in an empirical study concerning the measurement of conditional volatility from financial returns data.