On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns

Abstract

Using synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretched-Exponential distributions, it is shown that for samples of moderate sizes the standard generalized extreme value (GEV) estimator is quite inefficient due to the possibly slow convergence toward the asymptotic theoretical distribution and the existence of biases in the presence of dependence between data. Thus, it cannot distinguish reliably between rapidly and regularly varying classes of distributions. The Generalized Pareto distribution (GPD) estimator works better, but still lacks power in the presence of strong dependence. Applied to 100 years of daily returns of the Dow Jones Industrial Average and over one years of five-minutes returns of the Nasdaq Composite index, the GEV and GDP estimators are found insufficient to prove that the distributions of empirical returns of financial time series are regularly varying, because the rapidly varying exponential or stretched exponential distributions are equally acceptable.

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