Statistical Inference of 1D Persistent Nonlinear Time Series and Application to Predictions

TL;DR

This paper presents a novel method combining fractional calculus and Langevin equations to reconstruct and predict long-range correlated 1D stochastic processes, demonstrated on temperature data for frost date prediction.

Contribution

It introduces a new approach for reconstructing macroscopic models of 1D stochastic processes with long-range correlations from sparse data, applicable to temperature prediction.

Findings

Successfully reconstructed temperature models from sparse data.

Accurately predicted first frost date using the reconstructed model.

Demonstrated potential for subseasonal-to-seasonal predictions.

Abstract

We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The method is illustrated for the ARFIMA(1,d,0) process and a nonlinear auto-regressive toy model with multiplicative noise. We reconstruct a model for daily mean temperature data recorded at Potsdam (Germany) and use it to predict the first frost date by computing the mean first passage time of the reconstructed process and the zero degree Celsius temperature line, illustrating the potential of long-memory models for predictions in the subseasonal-to-seasonal range.