Kernel-based prediction of non-Markovian time series

A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider a supervised learning task finding regression function that takes delay-embedded observable the at future time. When delay-embedding theory applicable, proposed consistent estimator flow map induced by delay-embedding. Furthermore, corresponding Mori–Zwanzig equation governing evolution simplifies only Markovian term, represented function. We realize this with class kernel-based linear estimators, kernel analog forecast (KAF), which are in limit large data. In scenario high-dimensional covariate space, employ smoothing computationally cheaper than Nyström projection for realizing KAF. addition guaranteed theoretical convergence, numerically demonstrate effectiveness approach on higher-dimensional problems where relevant features difficult capture method. Given noisy training data, propose smoother as de-noising Numerically, show more accurate EnKF and 4Dvar signals corrupted independent (but not necessarily identically distributed) noise, even if constructed using data set white noise. skillful KAF from denoised