论文标题
基于β二项式自回归运动平均模型的信号检测和推理
Signal Detection and Inference Based on the Beta Binomial Autoregressive Moving Average Model
论文作者
论文摘要
本文提出了用于建模量化幅度数据和有界计数数据的β二项式自回归运动平均模型（BBARMA）。 BBARMA模型估计了通过动态结构观察到的β二项式分布式变量的条件平均值，包括：（i）自回归和移动平均项； （ii）一组回归器； （iii）链接函数。除了引入新模型外，我们还开发了参数估计，检测工具，信号预测方案和诊断措施。特别是，我们为条件分数向量和条件信息矩阵提供了封闭形式的表达式。提出的模型被提交给广泛的蒙特卡洛模拟，以评估条件最大似然估计器和拟议检测器的性能。衍生的检测器的表现优于正弦信号检测的通常基于ARMA和高斯的检测器。我们还提出了一个实验，用于建模和预测巴西雷·巴西的雨天数量。
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.
