10.6084/m9.figshare.3179869 Francisco Blasques Francisco Blasques André Lucas André Lucas Erkki Silde Erkki Silde A stochastic recurrence equations approach for score driven correlation models Taylor & Francis Group 2016 Asymptotic normality consistency dynamic copulas generalized autoregressive score models observation driven models stochastic recurrence equations C22 C32 C58 2016-04-15 15:55:50 Journal contribution https://tandf.figshare.com/articles/journal_contribution/A_stochastic_recurrence_equations_approach_for_score_driven_correlation_models/3179869 <p>We describe stationarity and ergodicity (SE) regions for a recently proposed class of score driven dynamic correlation models. These models have important applications in empirical work. The regions are derived from sufficiency conditions in Bougerol (<a href="#CIT0008" target="_blank">1993</a>) and take a nonstandard form. We show that the nonstandard shape of the sufficiency regions cannot be avoided by reparameterizing the model or by rescaling the score steps in the transition equation for the correlation parameter. This makes the result markedly different from the volatility case. Observationally equivalent decompositions of the stochastic recurrence equation yield regions with different shapes and sizes. We use these results to establish the consistency and asymptotic normality of the maximum likelihood estimator. We illustrate our results with an analysis of time-varying correlations between U.K. and Greek equity indices. We find that also in empirical applications different decompositions can give rise to different conclusions regarding the stability of the estimated model.</p>