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Unit-Weibull autoregressive moving average models

Author

Listed:
  • Guilherme Pumi

    (Mathematics and Statistics Institute and Programa de Pós-Graduação em Estatística - Universidade Federal do Rio Grande do Sul)

  • Taiane Schaedler Prass

    (Mathematics and Statistics Institute and Programa de Pós-Graduação em Estatística - Universidade Federal do Rio Grande do Sul)

  • Cleiton Guollo Taufemback

    (Mathematics and Statistics Institute and Programa de Pós-Graduação em Estatística - Universidade Federal do Rio Grande do Sul)

Abstract

In this work we introduce the class of Unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in (0, 1). The proposed model is an observation driven one, for which, conditionally on a set of covariates and the process’ history, the random component is assumed to follow a Unit-Weibull distribution parameterized through its $$\rho $$ ρ th quantile. The systematic component prescribes an ARMA-like structure to model the conditional $$\rho $$ ρ th quantile by means of a link. Parameter estimation in the proposed model is performed using partial maximum likelihood, for which we provide closed formulas for the score vector and partial information matrix. We also discuss some inferential tools, such as the construction of confidence intervals, hypotheses testing, model selection, and forecasting. A Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed partial maximum likelihood approach. Finally, we examine the prediction power by contrasting our method with others in the literature using the Manufacturing Capacity Utilization from the US.

Suggested Citation

  • Guilherme Pumi & Taiane Schaedler Prass & Cleiton Guollo Taufemback, 2024. "Unit-Weibull autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 204-229, March.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:1:d:10.1007_s11749-023-00893-8
    DOI: 10.1007/s11749-023-00893-8
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    References listed on IDEAS

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    1. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    2. Andréa V. Rocha & Francisco Cribari-Neto, 2017. "Erratum to: Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 451-459, June.
    3. Hamid Baghestani, 2008. "Predicting capacity utilization: Federal Reserve vs time-series models," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 32(1), pages 47-57, January.
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    15. Guilherme Pumi & Cristine Rauber & Fábio M. Bayer, 2020. "Kumaraswamy regression model with Aranda-Ordaz link function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1051-1071, December.
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