Evolution of Statistical Methods in Financial Time Series Analysis: An Empirical Analysis from ARIMA to the GARCH Family of Models

Abstract

Financial time series analysis is one of the key tools for asset pricing and forecasting, and its statistical methods have been continuously developing according to market demand. In the early days, the ARIMA model had great advantages in macro data analysis through its assumptions of linearity, homoscedasticity, and stationarity. Its stationary linear model was often used to predict shortterm economic indicators. However, as market products gradually emerged, non-linear and highly volatile data gradually dominated the trading market, indicating that the ARIMA model was unable to characterize non-linear characteristics such as volatility clustering, asymmetric leverage effects, spike tails, and long memory, which became increasingly apparent. Therefore, the academic community has successively introduced models based on nonlinear assumptions such as ARCH, GARCH family models, EGARCH, TGARCH, and FIGARCH, which have achieved accurate prediction of financial market risks. This article conducts a literature review and comparative analysis to study the evolution, improvement, and application of ARIMA models from traditional ARIMA models to GARCH family models. It explores the advantages and limitations of ARIMA model in modeling financial time series analysis statistics, and GARCH improves the modeling framework. It summarizes the impact of its development on financial time series analysis and provides a selection of modeling methods for financial analysis.