Statistical inference of one-dimensional persistent nonlinear time series and application to 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 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^{∘}C temperature line, illustrating the potential of long-memory models for predictions in the subseasonal-to-seasonal range.