On testing for non-linear and time irreversible probabilistic structure in high frequency ASX financial time series data

In this paper, we present three nonparametric trispectrum tests that can establish whether the spectral decomposition of kurtosis of high frequency financial asset price time series is consistent with the assumptions of Gaussianity, linearity and time reversiblility. The detection of nonlinear and time irreversible probabilistic structure has important implications for the choice and implementation of a range of models of the evolution of asset prices, including Black-Sholes-Merton (BSM) option pricing model, ARCH/GARCH and stochastic volatility models. We apply the tests to a selection of high frequency Australian (ASX) stocks.