Kumaraswamy autoregressive moving average models for double bounded environmental data

• Published in: Journal of hydrology (Amsterdam) 2017-12, Vol.555, p.385-396
• Main Authors: Bayer, Fábio Mariano, Bayer, Débora Missio, Pumi, Guilherme
• Format: Article
• Language: English
• Subjects: ARMA; Double bounded data; Dynamic model; Forecasts; Kumaraswamy distribution
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2017.10.006

•This paper introduces the Kumaraswamy autoregressive moving average models (KARMA).•KARMA is a dynamic model for time series following the Kumaraswamy distribution.•Conditional likelihood inference, diagnostic analysis and forecasting are considered.•A Monte Carlo simulation study is considered.•An application to environmental real data is presented and discussed. 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.