A multivariate conditional autoregressive range model

This paper proposes a multivariate extension of the conditional autoregressive range (CARR) model recently proposed in the literature. The CARR model provides an interesting alternative to the traditional volatility models (e.g. GARCH and stochastic volatility). We derive conditions for the existence of the first moment, stationarity, geometric ergodicity and beta-mixing property with exponential decay for the multivariate CARR.