Time-dependent scaling patterns in high frequency financial data

Abstract

Abstract. 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.

Financial Time Series Forecasting Using Empirical Mode Decomposition and Support Vector Regression

“…There are several implementations for EMD in the literature; in this paper, we adopt a variation of the procedure introduced by Flandrin and Gonçalves (2004); Huang et al (1998). The interested reader can see our previous papers (Nava et al 2016a(Nava et al , 2017 for further details). Typically in the EMD, the number of IMF components n is automatically discovered by the method, which stops when only a nonoscillating residual is left.…”

“…There are two major challenges associated with forecasting financial time series: (1) nonstationarity (i.e., the statistical properties of the time series change with time); (2) multi-scaling (i.e., the statistical properties of the time series change with time-horizons) (Di Matteo 2007;Nava et al 2016aNava et al , 2016b. EMD brings two elements that directly address both issues.…”

Two different flavours of complexity in financial data

“…A different approach to investigate scaling and multiscaling of financial time series which makes use of Empirical Mode Decomposition has been recently introduced [49]. This methodology has the advantage of being robust against non-stationarity and it provides a timedependent exponent [50].…”

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

“…[1][2][3][4][5]). Many works have been dedicated to its empirical characterization [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], reporting strong evidence of its presence in financial markets. Several models have been proposed [24][25][26][27][28][29][30][31][32][33] to reproduce these empirical facts.…”