J. P. Morgan RiskMetrics

 This model is basically a non-stationary GARCH(1,1) model. The GARCH coefficients are pre-defined by the RiskMetrics technology - and so no optimization is necessary. To be consistent with the previous 2 models - we choose a build up period of 250 days - although the effective model memory is much shorter due to the exponentially decaying weight of the moving average that the GARCH(1,1) process emulates. As in the previous 2 models - the analysis is based on the 1000 prediction-realization pairs constructed from the last 1251 data points in the 10 log differenced price change series k. For convenience we define $t\in[-249,0]$ as representing the build up period.