In this paper, we consider the estimation of the tail indices of distributions in the domain of attraction of stable laws. We follow the approach of Meerschaert and Scheffler (1999), which requires exclusively the spectral decomposition of the uncentered sample moment matrix containing the...

By considering pointwise maxima of independent stationary random processes with dependent Cauchy marginals, we define a new process whose univariate limit distributions are Fréchet and the bivariate distributions interpolate between independence and complete dependence. The limiting dependence...

We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests for the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis. The new tests are consistent against a large class of alternatives. A...

A new method for detecting regime switches between different probability distributions in financial time series is shown. In the proposed method, time series observations are divided into several segments, and a Gaussian model or a Cauchy model is fitted to each segment. The goodness of fit of...

We offer a new and straightforward proof of F.B. Knight's [3] theorem that the Cauchy type is characterized by the fact that it has no atom and is invariant under the involution i : x - -1/x. Our approach uses the representation X = tan theta where theta is uniform on (-pi/2,pi/2) when X is...

A limit theory is developed for mildly explosive autoregression under both weakly and strongly dependent innovation errors. We find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the in the form of the limiting distribution and, in...

We characterize uniform distributions on spheres in n-dimensional spacesL[alpha]by certain Cauchy-like (n-1)-dimensional distributions of the quotients and derive some properties of mixtures of uniform distributions on such spheres, i.e.,[alpha]-spherical distributions. We feel that a simple...