#QERMit
Quick Evaluation of Risk by Mixtures of t - a project originating from my MPhil thesis. Bayesian evaluation of Value at Risk and Expected Shortfall for a given volatility model. Modifiaction and extension of the paper by Hoogerheide and van Dijk (2010).
Modification: changing the underlying approximation algorithm from AdMit (Hoogerheide et al., 2007) to a more flexible and accurate one, MitISEM (Hoogerheide et al., 2012).
Extensions:
- to allow for nonlinear non-Gassian state space models (in the spirit of Barra et al., 2016) with the NAIS state sampler (Koopman et al., 2015);
- to allow for long run risk predictions (like one-month-ahead or one-year-ahead), based on partial candidate construction (with the Partial MitISEM algorithm of Hoogerheide et al., 2012).
To speed up computations, I "MEXed" some of the MATLAB codes (i.e. they are written in C).
###References
Barra, I., L. F. Hoogerheide, S. J. Koopman and A. Lucas (2016), "Joint Bayesian Analysis of Parameters and States in Nonlinear non-Gaussian State Space Models", Journal of Applied Econometrics, 31, forthcoming.
Hoogerheide, L. F., J. F. Kaashoek, and H. K. van Dijk (2007), "On the Shape of Posterior Densities and Credible Sets in Instrumental Variable Regression Models with Reduced Rank: an Application of Flexible Sampling Methods using Neural Networks", Journal of Econometrics, 139, 154-180.
Hoogerheide, L. F., A. Opschoor, and H. K. van Dijk (2012), "A Class of Adaptive Importance Sampling Weighted EM Algorithms for Effcient and Robust Posterior and Predictive Simulation", Journal of Econometrics, 171, 101-120.
Hoogerheide, L. F. and H. K. van Dijk (2010), "Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling", International Journal of Forecasting, 26, 231-247.
Koopman, S. J., A. Lucas and M. Scharth (2015), "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models", Journal of Business and Economic Statistics, 33, 114-127.