Abstract
ABSTRACTWe 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.
Highlights
Time-variation in correlations is an important feature of economic and nancial data and a crucial ingredient of empirical analyses, such as the assessment of risk and the construction of investment portfolios
We focus on the stochastic properties of the recently proposed score driven models of Creal et al (2011, 2013) and Harvey (2013), which we refer to as generalized autoregressive score (GAS) models
We provide a benchmark by estimating a simple exponentially weighted moving average (EWMA) scheme for the correlation based on the recursion ρt = tanh(ft) and ft+1 = ω + βft + (1 − β)y1ty2t, see the Gaussian dynamic copula speci cation of Patton (2006)
Summary
Time-variation in correlations is an important feature of economic and nancial data and a crucial ingredient of empirical analyses, such as the assessment of risk and the construction of investment portfolios. The score driven approach used in the construction of GAS models, provides a much more general and uni ed framework for parameter dynamics that is applicable far beyond the volatility and correlation context; see Creal et al (2013, 2014) for a range of other examples. We demonstrate that the conditions for nonlinear recurrence equations can be used to ensure stationarity of concrete models, applied on real data This extends the results in Blasques et al (2014b) for volatility and tail index models with univariate observations to the case of time-varying parameters and multivariate observations.
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