Learning Causally-Generated Stationary Time Series

TL;DR

This paper introduces the Causal Gaussian Process Convolution Model (CGPCM), a new nonparametric generative model for causal, spectrally complex time series, with improved inference methods validated on synthetic and real data.

Contribution

The paper proposes the CGPCM, a novel causal nonparametric Gaussian process model, and develops advanced variational inference techniques for better accuracy.

Findings

Enhanced inference schemes significantly improve statistical accuracy.

Demonstrated effectiveness on synthetic signals.

Validated on real-world time series data.

Abstract

We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal, nonparametric-window moving-average filter, a construction that we show to be equivalent to a Gaussian process with a nonparametric kernel that is biased towards causally-generated signals. We develop enhanced variational inference and learning schemes for the CGPCM and its previous acausal variant, the GPCM (Tobar et al., 2015b), that significantly improve statistical accuracy. These modelling and inferential contributions are demonstrated on a range of synthetic and real-world signals.