Functional gradient descent for financial time series with an application to the measurement of market risk

The estimation and forecast of the volatility matrix are two of the main tasks of financial econometrics since they are essential ingredients in many practical applications. Unfortunately the use of classical multivariate methods in large dimensions is difficult because of the curse of dimensionality. We present a general semiparametric technique, based on functional gradient descent (FGD) and able to overcome most problems associated with a multivariate GARCH-type estimation. By testing the accuracy of the volatility estimates for the measurement of market risk on real data we provide empirical evidence of the strong predictive potential of the FGD approach, also in comparison to other standard methods.