Journal of Data Science

Abstract: Until the late 70’s the spectral densities of stock returns and stock index returns exhibited a type of non-constancy that could be detected by standard tests for white noise. Since then these tests have been unable to find any substantial deviations from whiteness. But that does not mean that today’s returns spectra contain no useful information. Using several sophisticated frequency domain tests to look for specific patterns in the periodograms of returns series we find nothing or, more precisely, less than nothing. Actually, there is a striking power deficiency, which implies that these series exhibit even fewer patterns than white noise. To unveil the source of this “super-whiteness” we design a simple frequency domain test for characterless, fuzzy alternatives, which are not immediately usable for the construction of profitable trading strategies, and apply it to the same data. Because the power deficiency is now much smaller, we conclude that our puzzling findings may be due to trading activities based on excessive data snooping.

Abstract: Examining the daily Dow Jones Industrial Average (DJI) we find evidence both of higher-order anomalies and predictability. While most researchers are only aware of the relatively harmless anomalies that occur just in the mean, the first part of this article provides empirical evidence of more dangerous kinds of anomalies occurring in higher-order moments. This evidence casts some doubt on the common practice of fitting standard time series models (e.g., ARMA models, GARCH models, or stochastic volatility models) to financial time series and carrying out tests based upon autocorre lation coefficients without making proper provision for these anomalies. The second part of this article provides evidence in favor of the predictability of the returns on the DJI and, more interestingly, against the efficient market hypothesis. The special value of this evidence is due to the simplicity of the involved methods.