Statistical process control for the fractal dimension of a time series

摘要

The fractal dimension (FD) of a time series can be estimated to measure its self-similarity or complexity. By arbitrarily dividing a series of data in time and estimating the FD of each part one can monitor observations of complexity or self-similarity using statistical process control methods. After estimating FD through Suleymanov et al.'s approach and transforming the FD series into a normally distributed dataset, we finally show in the example that the transformed FD of a time series is well suited to statistical process control with respect to the normal distribution assumption and its expected Type I errors. And we conclude that fractal theory and process control can be integrated to objectively and systematically monitor the complexity of a time series.