# An early warning system for multivariate time series with sparse and non-uniform sampling

## TL;DR

This paper introduces the ratio of deviations (RoD), a new early warning statistic for multivariate systems, effective even with sparse, non-uniform, and high-frequency data, predicting bifurcations before they occur.

## Contribution

The paper proposes RoD, a novel early warning test statistic, and demonstrates its effectiveness in predicting Hopf bifurcations in complex, irregularly sampled multivariate time series.

## Key findings

- RoD is asymptotically related to autocorrelation.
- RoD effectively predicts bifurcations in synthetic sparse data.
- RoD performs well as a classifier on high-frequency time series.

## Abstract

In this paper we propose a new early warning test statistic, the ratio of deviations (RoD), which is defined to be the root mean squared of successive differences divided by the standard deviation. We show that RoD and autocorrelation are asymptotically related, and this relationship motivates the use of RoD to predict Hopf bifurcations in multivariate systems before they occur. We validate the use of RoD on synthetic data in the novel situation where the data is sparse and non-uniformly sampled. Additionally, we adapt the method to be used on high-frequency time series by sampling, and demonstrate the proficiency of RoD as a classifier.