Zero-inflated Rayleigh dynamical for SAR imagery and hydrological data modeling
Conference
65th ISI World Statistics Congress
Format: IPS Abstract - WSC 2025
Keywords: timeseries
Session: IPS 910 - Handling Time in Environmental Studies
Thursday 9 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
This paper introduces the zero-inflated Rayleigh seasonal autoregressive moving average model with exogenous regressors (iRSARMAX) for fitting and forecasting time series characterized by Rayleigh distribution and inflated zeros. The iRSARMAX model captures the conditional mean of the continuous component of the distribution using a dynamic framework that incorporates stochastic seasonality, autoregressive and moving average components, exogenous variables, and a link function. Simultaneously, it handles the zero-inflated portion through a parsimonious dynamic structure. The conditional maximum likelihood estimation of the model parameters is facilitated by deriving the analytical score vector, and the Fisher information matrix is used for hypothesis testing and constructing confidence intervals. Randomized quantile residuals are employed, and goodness-of-fit tests are conducted to validate the model's performance. A comprehensive simulation study demonstrates the robustness of the model in finite sample sizes. The proposed iRSARMAX model excels traditional seasonal autoregressive moving average models, and Holt-Winters filtering in forecasting influent flow and outperforms standard autoregressive moving average models in predicting synthetic aperture radar (SAR) image data.