Estimation for a class of positive nonlinear time series models

Abstract

This paper considers the a symptotic properties of an estimator of a parameter that generalizes the correlation coefficient to a class of nonlinear, non-Gaussian and positive time series models. The models considered are one step Markov chains whose innovations have an infinitely divisible distribution, as do the marginal distributions. The models and their statistical analysis do not degenerate as is the case for some linear models that have been suggested for positive time series data. The asymptotic theory derives from a point process weak convergence argument that uses a regular variation assumption on the left tail of the innovation distribution.