In this work we introduce a class of dynamic models for time series taking
values on the unit interval. The proposed model follows a generalized linear
model approach where the random component, conditioned on the past information,
follows a beta distribution, while the conditional mean specification may
include covariates and also an extra additive term given by the iteration of a
map that can present chaotic behavior. The resulting model is very flexible and
its systematic component can accommodate short and long range dependence,
periodic behavior, laminar phases, etc. We derive easily verifiable conditions
for the stationarity of the proposed model, as well as conditions for the law
of large numbers and a Birkhoff-type theorem to hold. A Monte Carlo simulation
study is performed to assess the finite sample behavior of the partial maximum
likelihood approach for parameter estimation in the proposed model. Finally, an
application to the proportion of stored hydroelectrical energy in Southern
Brazil is presented