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BeatLex: Summarizing and Forecasting Time Series with Patterns Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Forecasting and Granger Modelling with Non-linear Dynamical Dependencies

Authors : Magda Gregorová, Alexandros Kalousis, Stéphane Marchand-Maillet

Published in: Machine Learning and Knowledge Discovery in Databases

Publisher: Springer International Publishing

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Abstract

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.

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previous chapter Efficient Temporal Kernels Between Feature Sets for Time Series Classification
next chapter Learning TSK Fuzzy Rules from Data Streams
Footnotes
1
We extend the function \(x^2/y : \mathbb {R} \times \mathbb {R}_{+} \rightarrow \mathbb {R}_+\) to the point (0, 0) by taking the convention \(0/0 = 0\).
 
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Metadata
Title
Forecasting and Granger Modelling with Non-linear Dynamical Dependencies
Authors
Magda Gregorová
Alexandros Kalousis
Stéphane Marchand-Maillet
Copyright Year
2017
Book
Machine Learning and Knowledge Discovery in Databases

Print ISBN: 978-3-319-71245-1

Electronic ISBN: 978-3-319-71246-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-71246-8_33

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