Kumaraswamy autoregressive moving average models for double bounded environmental data

TL;DR

This paper introduces KARMA models, a new class of dynamic models for double bounded time series data, with applications in environmental and hydrological studies, including estimation, inference, and forecasting.

Contribution

The paper proposes the novel KARMA model class for bounded time series, incorporating autoregressive, moving average, regressors, and link functions, with detailed estimation and inference methods.

Findings

Effective modeling of double bounded environmental data.

Closed-form expressions for score and Fisher information.

Successful application to real environmental data.

Abstract

In this paper we introduce the Kumaraswamy autoregressive moving average models (KARMA), which is a dynamic class of models for time series taking values in the double bounded interval $(a,b)$ following the Kumaraswamy distribution. The Kumaraswamy family of distribution is widely applied in many areas, especially hydrology and related fields. Classical examples are time series representing rates and proportions observed over time. In the proposed KARMA model, the median is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and a link function. We introduce the new class of models and discuss conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. An application to environmental real data is presented and discussed.