2016/10/10 by Blasques, F, Gorgi, P, Koopman, S +1
#FOS: Economics and business #FOS: Mathematics #Statistical Finance (q-fin.ST) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1610.02863
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure the consistency of the maximum likelihood estimator for a wide class of observation-driven time series models. Our consistency results hold for both correctly specified and misspecified models. The practical relevance of the theory is highlighted in a set of empirical examples. We further obtain an asymptotic test and confidence bounds for the unfeasible " true " invertibility region of the parameter space.