Mathematical Modelling and Analysis of Nonlinear Tme Series

Abstract

Time series analysis contains various statistical and computational techniques for analyz ing data points collected sequentially over time. This methodology is crucial in fields such as finance, economics, environmental science, and healthcare, where understanding tempo ral patterns and relationships in data informs decision-making and helps solve real-world problems. By modeling time series data as stochastic processes, modern techniques offer powerful tools for identifying trends, seasonality, and underlying structures while enabling accurate forecasting. This thesis explores linear and nonlinear models, including ARIMA, threshold models, and Markov switching models, providing a comprehensive overview of their theoretical foundations and practical applications. Through these models, time se ries analysis facilitates a deeper understanding of dynamic real-world phenomena, making it an essential tool in contemporary data analysis and predictive modeling.