The models for testing and dating breaks in stock returns and volatilities often rely on the restrictive assumption of common breaks. This assumption suggests that a shift occurred due to common innovations. Models under this assumption can only be estimated simultaneously. This assumption may...

For risk management, implementing risk measures and backtesting them are essential tasks. Since the expected shortfall (ES) possesses coherence and tail sensitivity, the Basel Committee has raised the option to replace the classical risk measure value-at-risk (VaR) with ES. However, the...

We provide a simple identity that decomposes a product moment of multivariate normal random variables as a sum of various products of univariate moments of one of the random variables and multivariate moments of the other random variables. The new identity allows for much faster computation of...

Multivariate distributional forecasts have become widespread in recent years. To assess the quality of such forecasts, suitable evaluation methods are needed. In the univariate case, calibration tests based on the probability integral transform (PIT) are routinely used. However, multivariate...

We propose a new approach to evaluating copula-based multivariate density forecasts. Employing Hansen’s SPA test and conducting multiple comparisons of fully-parametric models, our approach accommodates possible misspecifications in the multivariate joint and the univariate marginal...

In this article we propose a testing procedure for multivariate threshold autoregression with the disturbances following conditional homoscedastic martingale difference sequences. Essentially, the discussed test statistics are an extension of the work of Chan and Tong (1990) and Chan (1991), as...

The traditional linear Granger causality test has been widely used to examine the linear causality among several time series in bivariate settings as well as multivariate settings. Hiemstra and Jones (1994) develop a nonlinear Granger causality test in a bivariate setting to investigate the...