Exploring Gegenbauer Autoregressive Moving Average (GARMA) Models in Time Series Analysis: A Tool for Long Memory Data
Introduction With the vast amount of time series data being generated across the globe, from financial markets and cryptocurrencies to climate and environmental sciences, effective modeling has become essential. Time series models play a crucial role in identifying future patterns, forecasting values, and uncovering the factors that influence these dynamic processes. While modern machine learning and deep learning models are increasingly applied in time series analysis, their lack of interpretability often limits their practical use. As a result, classical time series models such as AR, MA, ARIMA, and SARIMA remain widely used due to their transparency and ease of interpretability. However, these traditional models typically fail to capture long-term dependencies in the data, that is, relationships between observations that are far apart in time. This is where long memory time series models become valuable. Among them, Autoregressive Fracti...