Short-term Kullback–Leibler divergence analysis to extract unstable periods in financial time series

A new method is presented for estimating a short-term Kullback-Leibler divergence to analyze the statistical characteristics of significant fluctuations in financial time series. The short-term Kullback–Leibler divergence is derived by transforming variations in financial time series into binary symbolic dynamics. This method quantifies the extent to which the occurrence of significant fluctuations deviates from independent Bernoulli trials in short-term financial time series. The study presents the calculation results of short-term Kullback–Leibler divergence for the USD/JPY exchange rate and the Nikkei 225 Index. The proposed technique serves as a valuable tool for analyzing and characterizing rapid changes in financial dynamics, with potential applications in advancing the analysis of financial market behaviors and trends. Its applications extend to risk assessment and decision-making processes.