### Citation:

Shephard, Neil. Working Paper. “Some properties of the sample median of an in-fill sequence of events with an application to high frequency financial econometrics”.

median20220904.pdf | 716 KB | |

median20220902.zip | 2 KB |

### Abstract:

Using an in-fill argument, the properties of the sample median of a sequence of events are established both for the case of a fixed period of time and for a period which shrinks as the sample size grows. The results are used to study the properties of the sample median of absolute returns under stochastic volatility. This estimator is invariant, asymptotically pivotal and a 1/2 breakdown estimator. In practice it has deep robustness to jump processes even when there are jumps of α-stable type.*Last updated on 09/04/2022*