Raubitzek, S.; Neubauer, T.; Friedrich, J.; Rauber, A. Interpolating Strange Attractors via Fractional Brownian Bridges. Entropy2022, 24, 718.
Raubitzek, S.; Neubauer, T.; Friedrich, J.; Rauber, A. Interpolating Strange Attractors via Fractional Brownian Bridges. Entropy 2022, 24, 718.
We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.
time series interpolation; phase space reconstruction; takens’ theorem; interpolation; stochastic interpolation; genetic algorithm; time series data; preprocessing; strange attractor; attractor; attractor reconstruction
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