Volatility Analysis of Financial Time Series Using the Multifractal Conditional Diffusion Entropy Method

In this article, we introduce the multifractal conditional diffusion entropy method for analyzing the volatility of financial time series. This method utilizes a q-order diffusion entropy based on a q-weighted time lag scale. The technique of conditional diffusion entropy proves valuable for examining bull and bear behaviors in stock markets across various time scales. Empirical findings from analyzing the Dow Jones Industrial Average (DJI) indicate that employing multi-time lag scales offers greater insight into the complex dynamics of highly fluctuating time series, often characterized by multifractal behavior. A smaller time scale like t=2 to t=256 coincides more with the state of the DJI index than larger time scales like t=256 to t=1024. We observe extreme fluctuations in the conditional diffusion entropy for DJI for a short time lag, while smoother or averaged fluctuations occur over larger time lags.