Chair of Statistics

FGD Code: A Program for Nonparametric High-Dimensional Time Series Analysis.

Author: Francesco Audrino,


  • Nonparametric time series, nonlinear time series, high-dimensional conditional mean and variance estimation


  • S-PLUS 6.1: Code and Help Word files for the functions of interest are available here. The code is provided at no charge for research purposes without warranty of any kind, expressed or implied.


  • Audrino, F., and Peter Bühlmann (2003)," Volatility estimation with Functional Gradient Descent for very high-dimensional financial time series," Journal of Computational Finance 6, No. 3, 65--89.
  • Audrino, F., and Giovanni Barone-Adesi (2005)," A multivariate FGD technique to improve VaR computation in equity markets, " Computational Management Science 2, 87--106.
  • Audrino, F., Barone-Adesi, G., and Antonietta Mira (2005)," The stability of factor models of interest rates," Journal of Financial Econometrics 3, No. 3, 422--441.
  • Audrino, F. (2006)," The impact of general non-parametric volatility functions in multivariate GARCH models," Computational Statistics and Data Analysis 50, No. 3, 3032--3052.
  • Audrino, F., and Fabio Trojani (2007)," Accurate Short-Term Yield Curve Forecasting using Functional Gradient Descent," Journal of Financial Econometrics 5, No. 4, 591--623.


  • Functional Gradient Descent (FGD) is a method of nonparametric time series analysis, useful in particular for estimating conditional mean, variances and covariances for very high-dimensional time series. FGD is a kind of hybrid of nonparametric statistical function estimation and numerical optimization. In fact, the idea of FGD comes from the fact that boosting can be viewed as an optimization algorithm in function space. This method employs an iterative refitting of generalized residuals, based on a given statistical procedure called base learner, to approximate the first two conditional moment functions of a multivariate process. An appealing feature of this expansion is that it is a nonlinear nonparametric model that directly nests the Gaussian diagonal VAR model, the Gaussian GARCH model and the multivariate CCC-GARCH as simple, starting special cases. The FGD model is fitted using conventional maximum likelihood together with a cross-validation strategy that determines the appropriate number of additive terms in the final expansions.


  • S,R


  • S-PLUS 6.1 for Windows is supported on Windows 98, Windows ME, and Windows XP Professional, and on Windows NT 4.0 and Windows 2000 running on Intel platforms. The minimum recommended system configuration is Pentium II/233 with 96MB of RAM. You must have at least 256MB of free disk space for the typical installation (and, if not installing on drive C:\, an additional 75MB free disk space on drive C:\ to unpack the distribution).


New optimized R codes available:

  • Codes have been optimized by Jan Siml during the writing of his master thesis. The new codes include also DCC, ACC, and TACC model functions with/without FGD.

© Raffo.