This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently...

A multivariate CVAR(1) model for some observed variables and some unobserved variables is analysed using its infinite order CVAR representation of the observations. Cointegration and adjustment coefficients in the infinite order CVAR are found as functions of the parameters in the CVAR(1) model....

This paper examines the heteroskedasticity and autocorrelation consistent (HAC) estimation of the long-run variance (LRV) matrix of a random vector process in a GMM estimation framework via vector autoregression (VAR) model averaging. By combining a VAR representation of GMM moments and VAR...

This paper theoretically and empirically analyzes backtesting portfolio VaR with estimation risk in an intrinsically multivariate framework. For the fi rst time in the literature, it takes into account the estimation of portfolio weights in forecasting portfolio VaR and its impact on...

Extreme Value Theory (EVT) deals with the analysis of rare events and it has been recently used in finance to predict the occurrence of such events, or, at least, to build more robust models for unexpected extreme events. Particularly, EVT has been used to model the loss severities in...

Historical Simulation (HS) and its variant, the Filtered Historical Simulation (FHS), are the most widely used Value-at-Risk forecast methods at commercial banks. These forecast methods are traditionally evaluated by means of the unconditional backtest. This paper formally shows that the...

In this note it is argued that the estimation error in Value-at-Risk predictors gives rise to underestimation of portfolio risk. We propose a simple correction and end in an empirical illustration that it is economically relevant

Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not quantify the risk beyond VaR, while CVaR shows some computational instabilities and is not 'elicitable' (Gneiting 2010, Ziegel 2013). It is argued in...

We propose a widely applicable bootstrap based test of the null hypothesis of equality of two firms' Risk Measures (RMs) at a single point in time. The test can be applied to any market-based measure. In an iterative procedure, we can identify a complete grouped ranking of the RMs, with...