  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.
