Forecasting and Granger Modelling with Non-linear Dynamical Dependencies
This provides a new alternative to existing graphical Granger techniques for researchers and practitioners dealing with non-Gaussian time series forecasting.
The authors tackled the problem of forecasting multivariate time series with non-linear dependencies by developing a method based on learning vector-valued functions in reproducing kernel Hilbert spaces, which learns both predictive functions and matrix-valued kernels directly from data. The method achieved superior predictive performance in the presence of strong non-linearities and recovered hidden dynamic relationships between series.
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction functions that accommodate such non-linearities. The method not only learns the predictive function but also the matrix-valued kernel underlying the function search space directly from the data. Our approach is based on learning multiple matrix-valued kernels, each of those composed of a set of input kernels and a set of output kernels learned in the cone of positive semi-definite matrices. In addition to superior predictive performance in the presence of strong non-linearities, our method also recovers the hidden dynamic relationships between the series and thus is a new alternative to existing graphical Granger techniques.