This paper develops a new test to evaluate Value at Risk (VaR) forecasts. VaR is a standard risk measure widely utilized by financial institutions and regulators, yet estimating VaR is a challenging problem, and popular VaR forecast relies on unrealistic assumptions. Hence, assessing the performance of VaR is of great importance. We propose the geometric-VaR test which utilizes the duration bet...

Real economic data always present nonlinear properties such as asymmetry and radically change in the series through time. Missing data and jumps as well as breaks also common reported in economic time series model. Thus, linear models are no longer suitable used in estimate the economic data and markov switching vector autoregressive model (MS-VAR) is applied in study the economic model. This p...

VAR models are popular to forecast macroeconomic time series. However, the model, parameters, and error distribution rarely known without uncertainty, so bootstrap methods applied deal with these sources of uncertainties. In this paper, performance Bonferroni cubes based on Gaussian method variants procedure that incorporate distribution, parameter bias correction, lag order uncertainty compare...

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. In fact, we demonstrate that only a few coefficients of the approximation ...

A new approach for using Lévy processes to compute value at risk (VaR) using high-frequency data is presented in this paper. The approach is a parametric model using an ARMA(1,1)-GARCH(1,1) model where the tail events are modeled using the fractional Lévy stable noise and Lévy stable distribution. Using high-frequency data for the German DAX Index, the VaR estimates from this approach are compa...

To capture the missed information in the standardized errors by parametric multivariate generalized autoregressive conditional heteroskedasticity (MV-GARCH) model, we propose a new semiparametric MV-GARCH (SM-GARCH) model. This SM-GARCH model is a twostep model: firstly estimating parametric MV-GARCH model, then using nonparametric skills to model the conditional covariance matrix of the standa...

In this chapter we give an introduction to different types of Ensemble Kalman filter, describe the Local Ensemble Transform Kalman Filter (LETKF) as a representative prototype of these methods, and several examples of how advanced properties and applications that have been developed and explored for 4D-Var (four-dimensional variational assimilation) can be adapted to the LETKF without requiring...