Statistical inference of one-dimensional persistent nonlinear time series and application to predictions

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 autoregressive 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 0 degrees C temperature line, illustrating the potential of long-memory models for predictions in the sub seasonal-to-seasonal range.

Automated summary

This study introduces a method that combines fractional calculus and discrete-time Langevin equations to reconstruct macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series. The method is demonstrated using specific examples, showing the potential application of long-memory models in short-term to seasonal predictions.