Testing for Non-linear and Time Irreversible Probabilistic Structure in High Frequency Financial Time Series Data

Summary We present three non-parametric 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 non-linear 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–Scholes–Merton option pricing model, auto-regressive conditional heteroscedastic or generalized auto-regressive conditional heteroscedastic and stochastic volatility models. We apply the tests to a selection of high frequency Australian stocks.