Fourth order cumulant in EUR/USD falsifies random walk hypothesis

Source: forexautomaton.com

Ability to predict the up-coming changes in daily and hourly high and low of price (of course, in a statistical sense, as measured by correlation coefficients between prediction and reality) by using adaptive black-box models has been well documented on this site. Observation of statistical dependence of the extreme levels of price (high and low) within a time bin on the immediate past of the time series, reported for the random walk model, explains and, particularly in the context of searching for market inefficiencies, even trivializes this achievement. Indeed, market inefficiencies are not required for the diffusion equation (cf. Black-Scholes theory) to work. Are we merely creating black-box equivalents of the popular tools of financial engineering? Enter higher-order cumulants. Shown here are measurements of the fourth order cumulants among the 24-hour high and low and the respective forecasts in real-life EUR/USD data; these can now be compared with the values they had in the random walk data. The difference revealed is dramatic.


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