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

Beran, Jan; Feng, Yuanhua; Ghosh, Sucharita

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

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Date

2015

Authors

Beran, Jan

Feng, Yuanhua

Ghosh, Sucharita

DOI (citable link)

10.1007/s00362-014-0590-x

Collections

Mathematik und Statistik

Publication type

Journal article

Published in

Statistical Papers ; 56 (2015), 2. - pp. 431-451. - ISSN 0932-5026. - eISSN 1613-9798

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.

Subject (DDC)

510 Mathematics

Keywords

Long-memory MEM model, Exponential FARIMA, Exponential ACD, Exponential SEMIFAR Nonparametric scale function Average durations

Cite This

ISO 690

BERAN, Jan, Yuanhua FENG, Sucharita GHOSH, 2015. Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models. In: Statistical Papers. 56(2), pp. 431-451. ISSN 0932-5026. eISSN 1613-9798. Available under: doi: 10.1007/s00362-014-0590-x

BibTex

@article{Beran2015Model-29162,
  year={2015},
  doi={10.1007/s00362-014-0590-x},
  title={Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models},
  number={2},
  volume={56},
  issn={0932-5026},
  journal={Statistical Papers},
  pages={431--451},
  author={Beran, Jan and Feng, Yuanhua and Ghosh, Sucharita}
}

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Bibliography of Konstanz

Yes