Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2011/09/P09003
Keywords
models of financial markets; stochastic processes; extreme value statistics
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We revisit the Kolmogorov-Smirnov and Cramer-von Mises goodness-of-fit (GoF) tests and propose a generalization to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the 'ffective' number of independent observations. The generalized GoF tests are not distribution-free but rather depend on all the lagged bivariate copulas. These objects, that we call 'self-copulas', encode all the non-linear temporal dependences. We introduce a specific, log-normal model for these self-copulas, for which a number of analytical results are derived. An application to financial time series is provided. As is well known, the dependence is to be long-ranged in this case, a finding that we confirm using self-copulas. As a consequence, the acceptance rates for GoF tests are substantially higher than if the returns were iid random variables.
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