65th ISI World Statistics Congress 2025

65th ISI World Statistics Congress 2025

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Autoregressive moving average model based on the Reflect Unit Burr XII distribution: theory and applications in hydroelectric energy forecasting

Author

RR
Renata Guerra

Co-author

Conference

65th ISI World Statistics Congress 2025

Format: IPS Abstract - WSC 2025

Keywords: time series

Session: IPS 910 - Handling Time in Environmental Studies

Thursday 9 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)

Abstract

This work introduces a new time series model based on the Reflected Unit Burr XII (RUBXII) distribution that is an alternative to the Kumaraswamy autoregressive moving average (KARMA) and beta autoregressive moving average (βARMA) models for time series analysis taking values in the standard unit interval. The proposed model describes the conditional median of RUBXII-distributed discrete-time series by a dynamic structure that includes autoregressive and moving average terms, a set of regressors, and a link function. We perform the model's parameter estimation using the conditional maximum likelihood method. Closed-form expressions for the score vector and observed information matrix are presented. We propose and discuss techniques of diagnostic and forecasting for the new model. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the conditional maximum likelihood estimator. Finally, the proportion of stored hydroelectric energy in Northern Brazil is analyzed through the proposed model. The results evidence that the RUBXII-ARMA model is suitable for describing the dynamics of the data and provides more accurate forecasts for the proportion of stored energy in Northern Brazil than those from competitors' models.

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