Beta seasonal autoregressive moving average models

TL;DR

This paper introduces beta seasonal autoregressive moving average ($\beta$SARMA) models for time series data within the unit interval, incorporating seasonality, and provides estimation, testing, diagnostics, and forecasting tools.

Contribution

It extends beta ARMA models by adding seasonal components, along with comprehensive estimation, inference, and diagnostic methods, including empirical evaluation.

Findings

Finite sample performance of estimators is validated via simulations.

The $\beta$SARMA$ model effectively captures seasonal patterns in data.

Empirical application demonstrates practical usefulness.

Abstract

In this paper we introduce the class of beta seasonal autoregressive moving average ($\beta$SARMA) models for modeling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha and Cribari-Neto, Test, 2009] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix. We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed.