  We measure the influence of different time-scales on the dynamics of
financial market data. This is obtained by decomposing financial time series
into simple oscillations associated with distinct time-scales. We propose two
new time-varying measures: 1) an amplitude scaling exponent and 2) an
entropy-like measure. We apply these measures to intraday, 30-second sampled
prices of various stock 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 open and close. We demonstrate that these deviations are
statistically significant and robust.
