Repair of physiologic time series: Replacement of anomalous data points to preserve fractal exponents

Extraction of fractal exponents via the slope of the power spectrum is common in the analysis of many physiological time series. The fractal structure thus characterized is a manifestation of long-term correlations, for which the temporal order of the sample values is crucial. However, missing data points due to artifacts and dropouts are common in such data sets, which can seriously disrupt the computation of fractal parameters. We evaluated a number of methods for replacing missing data in time series to enable reliable extraction of the fractal exponent and make recommendations as to the preferred replacement method depending on the proportion of missing values and any a priori estimate of the fractal exponent.