Hurst Exponent Estimation For Short-Time Series Based On Singular Value Decomposition Entropy

Complex time series appear commonly in a large diversity of the science, engineering, economy, financial and social fields. In many instances, complex time series exhibit scaling behavior over a wide range of scales. The traditional rescaled-range (R/S) analysis and the detrended fluctuation analysis (DFA) are commonly used to characterize the scaling behavior via the Hurst exponent. These methods perform well for long-time series. However, the performance may be poor for short times resulting from scarce measurements (e.g. less than a hundred). This work proposes an approach based on singular value decomposition (SVD) entropy for estimating the Hurst exponent for short-time series. In the first step, synthetic time series were used to find the relationship between Hurst exponent and SVD entropy. In the second step, an empirical relationship was proposed to estimate the Hurst exponent from SVD entropy computations of the time series. The performance of the approach was illustrated with two examples of real-time series (consumer price index (CPI) and El Niño Oceanic Index), showing that the estimated Hurst exponent provides valuable insights into the physical mechanisms involved in the generation of the time series.