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.

中文翻译：

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具有混沌驱动条件平均的双界时间序列的动态模型

在这项工作中，我们介绍了一类在单位间隔上取值的时间序列的动态模型。所提出的模型遵循广义线性模型方法，其中以过去信息为条件的随机分量遵循 beta 分布，而条件均值规范可能包括协变量以及由地图迭代给出的额外加性项，可以呈现混乱行为。由此产生的模型非常灵活，它的系统组件可以适应短程和长程相关性、周期性行为、层流相等。我们为所提出的模型的平稳性推导出了容易验证的条件，以及大数定律和一个 Birkhoff 型定理成立。执行蒙特卡罗模拟研究以评估在所提出的模型中用于参数估计的部分最大似然方法的有限样本行为。最后，介绍了巴西南部水电储能比例的应用。