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

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 accom-modate 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. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this work, a dynamical model is presented for conditionally symmetric time series with a long range dependent structure for the conditional mean. The proposed model specifies a symmetric underlying distribution of the time series, conditioned on its past. The conditional mean accommodates a long range dependent structure and a set of (possibly time dependent) regressors following an ARFIMA-like design. The study provides conditions for model existence and stationarity, as well as closed formulas for the unconditional mean, variance, and covariance structure. Parameter estimation utilizes partial likelihood and closed forms are obtained for the score vector and Hessian. A finite sample study of the proposed partial likelihood estimation is conducted. An application to real data related to wind speed in specific locations in Brazil is also presented.