Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models

Abstract

Duration series often exhibit long-range dependence and local nonstationarities. Here, exponential FARIMA (EFARIMA) and exponential SEMIFAR (ESEMIFAR) models are introduced. These models capture simultaneously nonstationarities in the mean as well as short- and long-range dependence, while avoiding the complication of unobservable latent processes. The models can be thought of as locally stationary long-memory extensions of exponential ACD models. Statistical properties of the models are derived. In particular the long-memory parameter in the original and the log-transformed process is the same. For Gaussian innovations, exact explicit formulas for all moments and autocovariances are given, and the unconditional distribution is log-normal. Estimation and model selection can be carried out with standard software. The approach is illustrated by an application to average daily transaction durations.