This paper proposes the beta binomial autoregressive moving average model (BBARMA) for modeling quantized amplitude data and bounded count data. The BBARMA model estimates the conditional mean of a beta binomial distributed variable observed over the time by a dynamic structure including: (i) autoregressive and moving average terms; (ii) a set of regressors; and (iii) a link function. Besides introducing the new model, we develop parameter estimation, detection tools, an out-of-signal forecasting scheme, and diagnostic measures. In particular, we provide closed-form expressions for the conditional score vector and the conditional information matrix. The proposed model was submitted to extensive Monte Carlo simulations in order to evaluate the performance of the conditional maximum likelihood estimators and of the proposed detector. The derived detector outperforms the usual ARMA- and Gaussian-based detectors for sinusoidal signal detection. We also presented an experiment for modeling and forecasting the monthly number of rainy days in Recife, Brazil.

翻译：本文提议了用于模拟量化振幅数据和约束性计数数据的乙二进制自动递减平均模型(BBARMA),BBARMA模型估计了由动态结构观测的乙二进制分布变量的有条件值,动态结构包括:(一) 自动递减和移动平均条件;(二) 一组递减和移动平均条件;(三) 链接功能。除了引入新模型外,我们还开发了参数估计、检测工具、超出信号预报计划以及诊断措施。特别是,我们为有条件的分数矢量和有条件的信息矩阵提供了闭式表达式。拟议模型已提交广泛的蒙特卡洛模拟,以评价有条件最大概率估计器和拟议探测器的性能。衍生探测器超过常规的ARMA-和高斯安探测器的类固信号探测功能。我们还介绍了巴西累西腓月度降雨日的模拟和预报实验。