# Forecasting and Granger Modelling with Non-linear Dynamical Dependencies

arXiv: https://arxiv.org/abs/1706.08811 · HTML: https://mlsanity.com/paper/1706.08811/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2017.

## Built on by (most cited first, 2 of 2)

- [Entangled Kernels -- Beyond Separability](https://mlsanity.com/paper/2101.05514/) (2021)
- [Transfer Entropy Bottleneck: Learning Sequence to Sequence Information Transfer](https://mlsanity.com/paper/2211.16607/) (2022)

## Abstract (arXiv)

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.