# 14-029/III (2014-03-04; 2017-10-23)

Author(s)
Francisco Blasques, VU University Amsterdam; Siem Jan Koopman, VU University Amsterdam; Andre Lucas, VU University Amsterdam
Keywords:
score-driven models, time-varying parameters, Markov processes, stationarity, invertibility, consistency, asymptotic normality
JEL codes:
C13, C22, C12

We establish the strong consistency and asymptotic normality of the maximum likelihood estimator for time-varying parameter models driven by the score of the predictive likelihood function. We formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality under both correct specification and mis-specification of the model. A detailed illustration is provided for a conditional volatility model with disturbances from the Student's t distribution.