Goodness-of-fit test for copulas

Copulas are often used in finance to characterize the dependence between assets. However, a choice of the functional form for the copula is an open question in the literature. This paper develops a goodness-of-fit test for copulas based on positive definite bilinear forms. The suggested test avoids the use of plug-in estimators that is the common practice in the literature. The test statistics can be consistently computed on the basis of V-estimators even in the case of large dimensions. The test is applied to a dataset of US large cap stocks to assess the performance of the Gaussian copula for the portfolios of assets of various dimension. The Gaussian copula appears to be inadequate to characterize the dependence between assets.

Monkeying with the Goodness-of-Fit Test

The familiar sigma(OBS - EXP) ^2/EXP goodness-of-fit measure is commonly used to test whether an observed sequence came from the realization of n independent identically distributed (iid) discrete random variables. It can be quite effective for testing for identical distribution, but is not suited for assessing independence, as it pays no attention to the order in which output values are received. This note reviews a way to adjust or tamper, that is, monkey-with the classical test to make it test for independence as well as identical distribution--in short, to test for both the i's in iid, using monkey tests similar to those in the Diehard Battery of Tests of Randomness (Marsaglia'95).

A Linear-Time Kernel Goodness-of-Fit Test

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein's method, meaning that it is not necessary to compute the normalising constant of the model. We analyse the asymptotic Bahadur efficiency of the new test, and prove that under a mean-shift alternative, our test always has greater relative efficiency than a previous linear-time kernel test, regardless of the choice of parameters for that test. In experiments, the performance of our method exceeds that of the earlier linear-time test, and matches or exceeds the power of a quadratic-time kernel test. In high dimensions and where model structure may be exploited, our goodness of fit test performs far better than a quadratic-time two-sample test based on the Maximum Mean Discrepancy, with samples drawn from the model.Comment: Accepted to NIPS 201

Goodness-of-Fit Test: Khmaladze Transformation vs Empirical Likelihood

This paper compares two asymptotic distribution free methods for goodness-of-fit test of one sample of location-scale family: Khmaladze transformation and empirical likelihood methods. The comparison is made from the perspective of empirical level and power obtained from simulations. When testing for normal and logistic null distributions, we try various alternative distributions and find that Khmaladze transformation method has better power in most cases. R-package which was used for the simulation is available online. See section 5 for the detail