Regensburg 2022 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 6: Data Analytics for Complex Systems (joint session DY/SOE)
SOE 6.4: Talk
Monday, September 5, 2022, 15:45–16:00, H18
Stochastic Interpolation of Sparsely Sampled Time Series by a Superstatistical Random Process and its Synthesis in Fourier and Wavelet Space — •Jeremiah Lübke1, Jan Friedrich2, and Rainer Grauer1 — 1Institute for Theoretical Physics I, Ruhr-University Bochum, Universtitätsstr. 150, 44801 Bochum, Germany — 2ForWind, Institute of Physics, University of Oldenburg, Küpkersweg 70, 26129 Oldenburg, Germany
A novel method is presented for stochastic interpolation of a sparsely sampled time signal based on a superstatistical random process generated from a Gaussian scale mixture. In comparison to other stochastic interpolation methods such as kriging, this method possesses strong non-Gaussian properties and is thus applicable to a broad range of real-world time series. A precise sampling algorithm is provided in terms of a mixing procedure that consists of generating a field u(ξ,t), where each component uξ(t) is synthesized with identical underlying noise but covariance Cξ(t,s) parameterized by a log-normally distributed parameter ξ. Due to the Gaussianity of each component uξ(t), standard sampling algorithms and methods to constrain the process on the sparse measurement points can be exploited. The scale mixture u(t) is then obtained by assigning each point in time t a ξ(t) and therefore a specific value from u(ξ,t), where logξ(t) is itself a realization of a Gaussian process with a correlation time large compared to the correlation time of u(ξ,t). Finally, a wavelet-based hierarchical representation of the interpolating paths is introduced, which is shown to provide an adequate method to locally interpolate large datasets.