Exhaustive search for perfect predictors in complex binary data

Authors:
Adam V. Adamopoulos
Affiliations:
Medical Physics Laboratory, Department of Medicine, Democritus University of Thrace, Alexandroupolis, Hellas
Venue:
NOLASC'05 Proceedings of the 4th WSEAS International Conference on Non-linear Analysis, Non-linear Systems and Chaos
Year:
2005

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Abstract

An exhaustive method for the detection of short-term perfect predictors in complex binary sequences is presented. As short-term perfect predictors we assume bit sequences that give risk-free prediction of the value of the next bit. The method was tested on binary data sets produced by applying a simple binary transformation on the data of the logistic function for a variety of values of the nonlinearity parameter r. Despite the chaotic nature of the logistic function and the complexity of the obtained binary sequences, an unexpected high number of prediction rules were detected. In some cases the predictability reached up to 100%. In the worst case, (for r = 4.0), the predictability is up to 33.3%. Finally, as it was found via extensive simulations the number of L-bit perfect predictors as a function of their bit-length L is given by the Fibonacci recursive formula.