### Abstract

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.

Original language | English |
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Pages (from-to) | 951-988 |

Number of pages | 38 |

Journal | Scandinavian Journal of Statistics |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 Dec 1 |

### Keywords

- 60G52
- 60J75
- drift estimation
- mighty convergence
- semimartingale noise
- small noise asymptotics
- stochastic differential equation
- threshold estimator MSC2010:62F12; 62M05

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty