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While time series forecasting techniques have been widely developed, the self-similar structure of data has not been adequately addressed. This research focuses on investigating self-similar structures in real-time air traffic data from Air India and Indigo's scheduled domestic flights, aiming to develop a suitable forecasting model for self-similar time series. Self-similarity has proven valuable, particularly in processes like ARFIMA, long-range dependence, and the Hurst parameter. This study explores the current understanding of self-similarity, its concepts, definitions, and applications, offering a roadmap for future research. The book consolidates past works on air traffic modeling using methods such as Box-Jenkins, Exponential Smoothing, and Artificial Neural Networks. It aims to present a comprehensive overview of time series forecasting developments, focusing on air traffic modeling, long-range dependence through self-similarity, and fitting ARFIMA to identify the most effective forecasting model.