Statistical Inferences for Generalized Pareto Distribution Based on Interior Penalty Function Algorithm and Bootstrap Methods and Applications in Analyzing Stock Data

Abstract

This paper studies the application of extreme value statistics (EVS) theory on analysis for stock data, based on interior penalty function algorithm and Bootstrap methods. The generalized Pareto distribution (GPD) models are considered in analyzing the closing price data of Shanghai stock market. The maximum likelihood estimates (MLEs) are obtained by using the interior penalty function algorithm. Correspondingly, the bias and standard errors of MLEs, and the hypothesis test on the shape parameter are concerned through Bootstrap methods. Some simulations are performed to demonstrate the efficacy of parameter estimation and the power of the test. The estimates of the tail index in this paper are compared with those obtained via classical methods. At last, the model is diagnosed by numerical and graphical methods and the Value-at-Risk (VaR) is estimated.