On the Extremes of Randomly Sub-Sampled Time Series

Abstract

In this paper, we investigate the extremal properties of randomly sub-sampled stationary sequences. Motivation comes from the need to account for the effect of missing values on the analysis of time series and the comparison of schemes for monitoring systems with breakdowns or systems with automatic replacement of devices in case of failures.

Keywords

• extreme value theory
• integer-valued stationary sequences
• sub-sampling
• failure
• extremal index