Goodness-of-Fit tests with Dependent Observations
| Autor: | Rémy Chicheportiche, Jean-Philippe Bouchaud |
|---|---|
| Přispěvatelé: | Science et Finance, Mathématiques Appliquées aux Systèmes - EA 4037 (MAS), Ecole Centrale Paris, Chaire de finance quantitative (FiQuant), Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec-CentraleSupélec |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Independent and identically distributed random variables Statistics::Theory Generalization FOS: Physical sciences Statistics::Other Statistics Bivariate analysis Statistics - Applications extreme value statistics FOS: Economics and business Goodness of fit Statistics Applications (stat.AP) Extreme value theory 05.40.-a 02.30.Lt 89.65.Gh 60F05 60G50 91B84 62M10 62P20 Condensed Matter - Statistical Mechanics Mathematics 91B84 62P20 62M10 60F05 [STAT.AP]Statistics [stat]/Applications [stat.AP] Statistical Finance (q-fin.ST) Statistical Mechanics (cond-mat.stat-mech) Stochastic process Univariate models of financial markets Quantitative Finance - Statistical Finance Statistical and Nonlinear Physics [QFIN.ST]Quantitative Finance [q-fin]/Statistical Finance [q-fin.ST] Statistics::Computation stochastic processes Statistics Probability and Uncertainty Random variable |
| Zdroj: | Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2011, 2011 (9), pp.P09003. ⟨10.1088/1742-5468/2011/09/P09003⟩ |
| ISSN: | 1742-5468 |
| DOI: | 10.1088/1742-5468/2011/09/P09003⟩ |
| Popis: | We revisit the Kolmogorov-Smirnov and Cram\'er-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. Comment: 26 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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