One Rule, No Randomness, and Nothing You Can Forecast
The map x to 4x(1-x) contains no randomness and is still useless for prediction, because substituting x = sin squared of pi t turns it into angle doubling: one binary digit of your measurement is spent per step, so fifty steps eat fifteen decimal digits. The resulting series has autocorrelation exactly zero at every lag, proved by orthogonality of distinct cosine frequencies rather than measured. What that does not establish is anything about real return series, and the article says so.