## Abstract

We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations, which are then discretized for numerical solution. The second is discrete in time, where one directly infers a discrete-time model in the form of a nonlinear autoregression moving average model. The comparison is performed in a special case where the observations are known to have been obtained from a hypoelliptic stochastic differential equation. We show that the discrete-time approach has better predictive skills, especially when the data are relatively sparse in time. We discuss open questions as well as the broader significance of the results.

Original language | English (US) |
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Pages (from-to) | 187-216 |

Number of pages | 30 |

Journal | Communications in Applied Mathematics and Computational Science |

Volume | 11 |

Issue number | 2 |

DOIs | |

State | Published - 2016 |

## Keywords

- Discrete partial data
- Hypoellipticity
- Kramers oscillator
- NARMA
- Statistical inference
- Stochastic parametrization

## ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics