Goodness-of-fit Tests With Dependent Observations
The authors 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. They 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 they call "Self-copulas", encode all the non-linear temporal dependences. They 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.