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Signal Detection and Inference Based on the Beta Binomial Autoregressive Moving Average Model
arXiv - MATH - Statistics Theory Pub Date : 2022-07-29 , DOI: arxiv-2208.00095
B. G. Palm, F. M. Bayer, R. J. Cintra

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.

中文翻译:

基于Beta二项式自回归移动平均模型的信号检测与推理

本文提出了用于对量化幅度数据和有界计数数据进行建模的 beta 二项式自回归移动平均模型 (BBARMA)。BBARMA 模型通过动态结构估计随时间观察到的 beta 二项分布变量的条件均值,包括: (i) 自回归和移动平均项;(ii) 一组回归量;(iii) 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、信号外预测方案和诊断措施。特别是,我们为条件得分向量和条件信息矩阵提供了封闭形式的表达式。将所提出的模型提交给广泛的蒙特卡罗模拟,以评估条件最大似然估计器和所提出的检测器的性能。派生的检测器在正弦信号检测方面优于通常的基于 ARMA 和高斯的检测器。我们还展示了一个模拟和预测巴西累西腓每月下雨天数的实验。
更新日期:2022-08-02
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