SYMARFIMA: A dynamical model for conditionally symmetric time series with long range dependence mean structure

Abstract

In this work we introduce a dynamical model for conditionally symmetric time series accommodating a long range dependent structure for the conditional mean. More specifically, the proposed model specify the underlying distribution of the time series, conditionally to its past, to be symmetric. The conditional mean is specified to accommodate a long range dependent structure, following an ARFIMA-like design, as well as a (possibly time dependent) set of regressors. We provide conditions for the existence and stationarity of the proposed model as well as closed formulas for its unconditional mean, variance and covariance structure. Parameter estimation is carried out via partial likelihood. The score vector and Hessian are obtained in closed forms. A finite sample study of the proposed partial likelihood estimation is carried out. To show the usefulness of the proposed model, we present an application to a real data set related to wind speed in certain locations in Brazil.