# Forecasting high-dimensional dynamics exploiting suboptimal embeddings

## TL;DR

This paper introduces a novel forecasting framework that leverages suboptimal embeddings optimized through combinatorial methods, outperforming existing approaches in high-dimensional nonlinear time series prediction across diverse datasets.

## Contribution

The paper presents a new forecasting method using suboptimal embeddings optimized by combinatorial algorithms, improving prediction accuracy over traditional embedding selection techniques.

## Key findings

- Outperforms existing frameworks on toy and real-world datasets.
- Applicable to various data lengths and dimensions.
- Effective across multiple fields like neuroscience, ecology, and finance.

## Abstract

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be applied to yield a single forecast combining multiple forecasts derived from various embeddings. However, the performance of these frameworks is not always satisfactory because they randomly select embeddings or use brute force and do not consider the diversity of the embeddings to combine. Herein, we develop a forecasting framework that overcomes these existing problems. The framework exploits various "suboptimal embeddings" obtained by minimizing the in-sample error via combinatorial optimization. The framework achieves the best results among existing frameworks for sample toy datasets and a real-world flood dataset. We show that the framework is applicable to a wide range of data lengths and dimensions. Therefore, the framework can be applied to various fields such as neuroscience, ecology, finance, fluid dynamics, weather, and disaster prevention.