Exploring the Role of ARMA Models in Forecasting Time-Series Data

The efficacy and adaptability of Autoregressive Moving Average (ARMA) models have cemented their status as a cornerstone in the exploration and prediction of time-based phenomena within varied scientific and industrial contexts. This review delves into the extensive use of ARMA models for predictive analytics, with particular emphasis on economic forecasting, engineering control systems, and environmental monitoring, among others. The ARMA model is recognized for its synthesis of computational efficiency and statistical precision, which proves invaluable in deciphering temporal relationships within stationary datasets. Our investigation focuses on the fundamental concepts that characterize ARMA frameworks, reviews recent progress in enhancing these models, and showcases their effective deployment in practical forecasting scenarios. Furthermore, we scrutinize the limitations associated with ARMA methodologies—including their dependence on linearity and stationarity premises—and explore possible extensions to enhance their relevance in more dynamic and non-linear contexts. This inquiry aims to enrich the ongoing development of tools for time-series analysis by addressing these challenges.