Volatility analysis for high frequency time series via dimension reduction and functional ARCH

This article carries out volatility analysis of high frequency financial time series data.Based on squares of intraday returns, both multi-dimensional and infinite dimensional volatility analysis are discussed.Specifically, for a multi-dimensional approach, interpretable dimension reduction for volatility is pursued using the so called partially-quantified principal component analysis (PCA).To illustrate infinite dimensional volatility analysis, functional volatility model, viz., functional ARCH (fARCH) is entertained for high frequency financial time series data.Interesting applications are made using post Covid-19 financial time series.Volatility for one minute high frequency KOSPI (Korea stock prices index) data ranging from January 2022 to July 2024 is analyzed to obtain both an interpretable partially-quantified PCA and functional ARCH (fARCH) configuration.