Method of moments estimators for the external index of a stationary time series

The extremal index theta, a number in the interval [0, 1], is known to be a measure of primal importance for analyzing the extremes of a stationary time series. New rank-based estimators for theta are proposed which rely on the construction of approximate samples from the exponential distribution with parameter theta that is then to be fitted via the method of moments. The new estimators are analyzed both theoretically as well as empirically through a large-scale simulation study. In specific scenarios, in particular for time series models with theta approximate to 1, they are found to be superior to recent competitors from the literature.