Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange

•Nonlinearity in Athens Exchange high-frequency returns is studied.•Intraday volatility periodicity is filtered via a Flexible Fourier Form.•ARMA–FIGARCH models show that return volatility is long memory and self-similar.•Nonlinear analysis shows that the filtered data are random.•The high-frequency data are nonlinear stochastic but not deterministic.

This study investigates empirically the presence of nonlinearities in the Athens Composite Share Price Index high-frequency returns. A preliminary analysis indicates that volatility exhibits a periodic intraday inverse JJ-shaped pattern, associated with the opening and closing of the market. Periodicity is then removed employing a Flexible Fourier Form. Subsequently, an ARMA–FIGARCH model over several frequencies yields that return volatility is long memory and self-similar. Nonlinear analysis with the use of the embedding dimension suggests that the filtered return process does not exhibit deterministic or higher-order stochastic nonlinearity. Rather, it is reminiscent of a random process. We conclude that the ACSPI data are nonlinear; however, nonlinearity is attributed to persistent ARCH effects.