Time-dependent scaling patterns in high frequency financial data

We measure the influence of different time-scales on the intraday dynamics of financial markets. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying measures of complexity: 1) an amplitude scaling exponent and 2) an entropy-like measure. We apply these measures to intraday, 30-second sampled prices of various stock market indices. Our results reveal intraday trends where different time-horizons contribute with variable relative amplitudes over the course of the trading day. Our findings indicate that the time series we analysed have a non-stationary multifractal nature with predominantly persistent behaviour at the middle of the trading session and anti-persistent behaviour at the opening and at the closing of the session. We demonstrate that these patterns are statistically significant, robust, reproducible and characteristic of each stock market. We argue that any modelling, analytics or trading strategy must take into account these non-stationary intraday scaling patterns.