Extreme Value Analysis of Multivariate High-Frequency Wind Speed Data

Abstract

In this article we analyze the extremal behavior of wind speed with a measurement frequency of 8 Hz, measured on three meteorological masts in Denmark. In the first part of this article we set up a conditional model for the time series consisting of threshold exceedances from maxima per second for two consecutive days. The model directly captures the nonstationary nature of wind speed during the day. Conditional on previous wind speed values with recorded exceedance, we assume a Markov-like structure for exceedances, where the conditional distribution follows the generalized Pareto distribution. In addition, we analyze the dependence structure in large wind speed values between different masts by using bivariate extreme value models. The initial motivation for this research was in the context of renewable energy. Specifically, the extremal dynamics of wind speed at small time scales plays a critical role for designing and locating turbines on wind farms.

Keywords:

• primary: 62G32
• secondary: 62M10
• 60G70
• 62-07 regression, etc. analysis

Keywords:

• Wind speed
• generalized Pareto distribution
• bivariate extreme value theory

Acknowledgments

The authors thank Martin Greiner (Aarhus University) and Gunnar C. Larsen (Risø National Laboratory–Technical University of Denmmark) for valuable hints and discussions. All authors gratefully acknowledge support by the TUM Institute for Advanced Study (TUM-IAS). The third author additionally thanks the International Graduate School of Science and Engineering (IGSSE) of the Technische Universität München for its support. The research of Richard A. Davis was also supported in part by the National Science Foundation grant DMS-1107031.