We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation...

We investigate the dynamics of the relationship between returns and extreme downside risk in different states of the market by combining the framework of Bali, Demirtas, and Levy (2009) with a Markov switching mechanism. We show that the risk-return relationship identified by Bali, Demirtas, and...

We present a framework focused on the interdependence of high-dimensional tail events. This framework allows us to analyse and quantify tail interdependence at different levels of extremity, decompose it into systemic and residual part and to measure the contribution of a constituent to the...

We propose new systematic tail risk measures constructed using two different approaches. The first extends the canonical downside beta and co-moment measures, while the second is based on the sensitivity of stock returns to innovations in market crash risk. Both tail risk measures are associated...

Tail interdependence is defined as the situation where extreme outcomes for some variables are informative about such outcomes for other variables. We extend the concept of multi-information to quantify tail interdependence at different levels of extremity, decompose it into systemic and...

Evaluating multiple sources of risk is an important problem with many applications in finance and economics. In practice this evaluation remains challenging. We propose a simple non-parametric framework with several economic and statistical applications. In an empirical study, we illustrate the...

We define tail interdependence as a situation where extreme outcomes for some variables are informative about such outcomes for other variables. We extend the concept of multiinformation to quantify tail interdependence, decompose it into systemic and residual interdependence and measure the...