Extreme Value Theory for Time Series using Peak-Over-Threshold method

Abstract

This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an estimation of value for the Expected Shortfall can be useful, and the application of these few concepts are valid for the most wide range of risk analysis, from the financial application to the operational risk assessment, through the analysis for climate time series; resolving the problem of borderline data.