混沌驱动的双界时间序列的条件渐近动力学模型
A Dynamic Model for Double Bounded Time Series With Chaotic Driven Conditional Averages
摘要：
在这项工作中，我们介绍了一类动态模型的时间序列采取的值上的单位时间间隔。所提出的模型遵循广义线性模型的方法，其中的随机分量，条件上的过去的信息，遵循β分布，而条件均值规格可能包括协变量，也可以呈现混沌行为的映射的迭代给出的额外的附加项。由此产生的模型是非常灵活的，其系统的组成部分可以容纳短期和长期的依赖性，周期性行为，层流阶段等，我们推导出易于验证的条件所提出的模型的平稳性，以及条件的大数定律和Birkhoff型定理举行。蒙特卡洛模拟研究进行评估的部分最大似然法的参数估计在所提出的模型的有限样本行为。最后，在巴西南部的存储水电能源的比例的应用。
英文摘要：
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.
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