  We present a method to infer the arbitrary space-dependent drift and
diffusion of a nonlinear stochastic model driven by multiplicative fractional
Gaussian noise from a single trajectory. Our method, fractional Onsager-Machlup
optimisation (fOMo), introduces a maximum likelihood estimator by minimising a
field-theoretic action which we construct from the observed time series. We
successfully test fOMo for a wide range of Hurst exponents using artificial
data with strong nonlinearities, and apply it to a data set of daily mean
temperatures. We further highlight the significant systematic estimation errors
when ignoring non-Markovianity, underlining the need for nonlinear fractional
inference methods when studying real-world long-range (anti-)correlated
systems.
