On the validity of conventional statistical tests given evidence of non-synchronous trading and non-linear dynamics in returns generating process

Abstract

Based on the recent developments in market microstructure and applications of nonlinear dynamics and chaos theory to financial time series, the subsequent article questions the validity of traditional methods used to test the efficient market hypothesis. In particular, it emphasizes the invalidity of unit roots tests since they are not predictability tests.

Notes

¹ Fama (1970, 1991, 2001) provides thorough surveys of this literature.

² The present study is concerned with the short-term predictability of future share price changes using only past price changes.

³ We use the natural logarithm of prices because it has the advantage of making the process generating the times series become independent of the actual price levels. Furthermore, p_t has favourable econometric properties in comparison to P_t (see Campbell et al., 1997).

⁴ Other studies such as of Hasbrouck and Ho (1987) explain the existence of autocorrelation by the lagged adjustment of limit-orders price. See also Campbell et al. (1993) for a modelling of autocorrelations in index and stock returns.

⁵ While Vaidyanathan and Krehbiel (1992) and Mayfield and Mizrach (1992) find evidence of chaos behaviour in the S&P 500 index, Abhyankar et al. (1997) and Serletis and Shintani (2003) reject the null hypothesis of low-dimensional chaos in S&P 500 and Dow Jones Industrial Average. Hsieh (1989, 1993), Tata (1991) and Serletis and Shahmoradi (2004) find no or little evidence of low-dimensional structure in exchange-rate series.

⁶ Schatzberg and Reiber (1992) suggest share prices do not always adjust instantaneously to new information.