Long correlations and fractional difference analysis applied to the study of memory effects in high-frequency (tick) data

This work is devoted to the study of long correlations, memory effects and other statistical properties of a sample of high-frequency (tick) data. The high-frequency data sample consists of high-frequency (minute) data for several stocks over a seven-day period which we know is relevant for market crush behaviour in the US market; 10–18 March 2008. The Hurst exponent estimation, the detrended fluctuation analysis and the fractional difference parameter are the tools used for this analysis. It also investigates the underlying volatility processes in high-frequency (tick) data using range of GARCH specifications. The GARCH variants considered include the basic GARCH, IGARCH, ARFIMA (0,,0)-GARCH and FIGARCH models. In all the applications, the methodology provides insight into features of these series volatility.