We introduce the smooth total variation distance as a natural choice to establish equivalence. We propose asymptotic and bootstrap-based tests for which asymptotic optimality is shown. The finite sample performance is studied by simulations. Then we apply tests to real data sets

This paper provides empirical results supporting the theoretical ones by the first author on backtesting long-horizon distributional forecasts. The problem is quite general but for us it is motivated by the regulatory requirement of backtesting evolution models used in the measurement of...

In this paper we address a challenging aspect that arises in the regulatory requirement of back-testing the accuracy of distributional forecasts. The latter are core to measurement and capitalization of counterparty risk for banks under the IMM (Internal Models Method). The problem is very...

We introduce the smooth total variation distance as a natural choice to establish equivalence. We propose asymptotic and bootstrap-based tests for which asymptotic optimality is shown. The finite sample performance is studied by simulations. Then we apply tests to real data sets. The tests are...

We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF)-inferred from noisy high-frequency data-is consistent as the mesh of the observation...

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian...

A new measure of asymmetry in dependence is proposed which is based on taking the difference between the margin-free coskewness parameters of the underlying copula. The new measure and a related test are applied to both a hydrological and a financial market data sample and we show that both...

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume...

Generalized autoregressive conditional heteroscedasticity (GARCH)-type models have been successively used to capture the conditional volatility of macroeconomic and financial time series in the past two decades. However, few diagnostic tests are specifically devised to check the adequacy of...

Let (X1, Y1), … , (Xn, Yn) be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima max( Xi) and max(Yi) is then characterized by the...