Signal Detection and Inference Based on the Beta Binomial Autoregressive Moving Average Model

TL;DR

This paper introduces the BBARMA model for analyzing bounded count and quantized amplitude data, providing new estimation, detection, and forecasting tools with demonstrated superior performance over traditional methods.

Contribution

The paper presents the novel BBARMA model, including its estimation, detection, and forecasting methods, with extensive simulation and real data application.

Findings

The detector outperforms ARMA- and Gaussian-based detectors in sinusoidal signal detection.

The model effectively captures the dynamics of bounded count data.

Simulation results confirm the accuracy of the maximum likelihood estimators.

Abstract

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.