Goodness-of-Fit tests with Dependent Observations

Rémy Chicheportiche () and Jean-Philippe Bouchaud ()
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Rémy Chicheportiche: Science et Finance - Science et Finance, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec
Jean-Philippe Bouchaud: Science et Finance - Science et Finance

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Abstract: We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised 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.

Keywords: stochastic processes; extreme value statistics; models of financial markets (search for similar items in EconPapers)
Date: 2011-09-05
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Citations: View citations in EconPapers (10)

Published in Journal of Statistical Mechanics: Theory and Experiment, 2011, 2011 (9), pp.P09003. ⟨10.1088/1742-5468/2011/09/P09003⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00621061

DOI: 10.1088/1742-5468/2011/09/P09003

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