A Robust Variance Complexity Measure for Stochastic Self-Affine Processes

The complexity of a deterministic differentiable process is lower than that of a stochastic nondifferentiable process. Measuring the complexity of such processes may be useful in extracting objective features from the processes for their classification in either reactive, adaptive, or predictive control. This applies to classifiers based not only on the traditional neural networks, but also on deep learning systems, and particularly in cognitive systems. This paper describes a robust algorithm to measure the variance complexity of a self-affine time series using multiscale and polyscale analyses, and provides new insight in the theoretical and practical aspects of extracting the measure.