Kumaraswamy autoregressive moving average models for double bounded 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.

25 pages, 4 tables, 4 figures

References in corpus (4)

• Improved estimators for a general class of beta regression models
• Beta regression for time series analysis of bounded data, with application to Canada Google${}^{\circledR }$ Flu Trends
• Bartlett corrections in beta regression models
• On quantile residuals in beta regression

Cited by in corpus (7)

• Signal Detection and Inference Based on the Beta Binomial Autoregressive Moving Average Model
• 2-D Rayleigh Autoregressive Moving Average Model for SAR Image Modeling
• A Dynamic Model for Double Bounded Time Series With Chaotic Driven Conditional Averages
• Unit-Weibull Autoregressive Moving Average Models
• Prediction Intervals in the Beta Autoregressive Moving Average Model
• Order selection in GARMA models for count time series: a Bayesian perspective
• A Matsuoka-Based GARMA Model for Hydrological Forecasting: Theory, Estimation, and Applications