Unit-Weibull Autoregressive Moving Average Models

TL;DR

This paper introduces unit-Weibull ARMA models for continuous data in (0,1), providing a new approach for modeling quantiles with comprehensive inference tools and demonstrating its effectiveness through simulations and real data.

Contribution

The paper proposes a novel unit-Weibull ARMA model for (0,1) data, including estimation, inference, and forecasting methods, with validation via simulations and real data analysis.

Findings

The model accurately estimates quantiles in simulations.

It outperforms existing methods in predictive power on real data.

The proposed inference procedures are effective and reliable.

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 $\rho$th quantile. The systematic component prescribes an ARMA-like structure to model the conditional $\rho$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.