A stochastic recurrence equations approach for score driven correlation models
研究了一类得分驱动动态相关模型的平稳性和遍历性区域，证明了其非标准形状无法通过重参数化或缩放得分步长来消除，并建立了极大似然估计的一致性和渐近正态性，应用于英国与希腊股指的时变相关性分析。
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 (1993) 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.