  Bounded time series consisting of rates or proportions are often encountered
in applications. This manuscript proposes a practical approach to analyze
bounded time series, through a beta regression model. The method allows the
direct interpretation of the regression parameters on the original response
scale, while properly accounting for the heteroskedasticity typical of bounded
variables. The serial dependence is modeled by a Gaussian copula, with a
correlation matrix corresponding to a stationary autoregressive and moving
average process. It is shown that inference, prediction, and control can be
carried out straightforwardly, with minor modifications to standard analysis of
autoregressive and moving average models. The methodology is motivated by an
application to the influenza-like-illness incidence estimated by the
Google${}^\circledR$ Flu Trends project.
