Unit-Weibull autoregressive moving average models

Guilherme Pumi (), Taiane Schaedler Prass () and Cleiton Taufemback
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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

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 1, No 13, 204-229

Abstract: 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.

Keywords: Time series analysis; Regression models; Partial maximum likelihood; Non-Gaussian time series; 62M10; 62F12; 62E20; 62G20; 60G15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00893-8

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