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A multivariate conditional autoregressive range model. (English) Zbl 1255.62244
Summary: We propose 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.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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