IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i3d10.1007_s00362-023-01459-4.html
   My bibliography  Save this article

Parametric quantile autoregressive moving average models with exogenous terms

Author

Listed:
  • Alan Dasilva

    (Universidade de São Paulo)

  • Helton Saulo

    (Universidade de Brasília
    University of Texas at Arlington)

  • Roberto Vila

    (Universidade de Brasília)

  • Jose A. Fiorucci

    (Universidade de Brasília)

  • Suvra Pal

    (University of Texas at Arlington)

Abstract

Parametric autoregressive moving average models with exogenous terms (ARMAX) have been widely used in the literature. Usually, these models consider a conditional mean or median dynamics, which limits the analysis. In this paper, we introduce a class of quantile ARMAX models based on log-symmetric distributions. This class is indexed by quantile and dispersion parameters. It not only accommodates the possibility to model bimodal and/or light/heavy-tailed distributed data but also accommodates heteroscedasticity. We estimate the model parameters by using the conditional maximum likelihood method. Furthermore, we carry out an extensive Monte Carlo simulation study to evaluate the performance of the proposed models and the estimation method in retrieving the true parameter values. Finally, the proposed class of models and the estimation method are applied to a dataset on the competition “M5 Forecasting - Accuracy” that corresponds to the daily sales history of several Walmart products. The results indicate that the proposed log-symmetric quantile ARMAX models have good performance in terms of model fitting and forecasting.

Suggested Citation

  • Alan Dasilva & Helton Saulo & Roberto Vila & Jose A. Fiorucci & Suvra Pal, 2024. "Parametric quantile autoregressive moving average models with exogenous terms," Statistical Papers, Springer, vol. 65(3), pages 1613-1643, May.
  • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01459-4
    DOI: 10.1007/s00362-023-01459-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01459-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00362-023-01459-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01459-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.