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.
Highlights
Delay embedding—a method for reconstructing dynamical systems by delay coordinates—is widely used to forecast nonlinear time series as a model-free approach
Ensembles tend to yield better results with significant diversity among its members[11,12], randomly distributed embedding (RDE) only aggregates forecasts for a fixed embedding dimension with a fixed number of embeddings to combine, regardless of their forecast performance. We propose another forecasting framework that overcomes the disadvantages of multiview embedding (MVE) and RDE
The principal concept is the same as those of MVE and RDE, the procedure to yield the multiple embeddings differs from the existing ones
Summary
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. Ma et al.[10] presented an outstanding framework, randomly distributed embedding (RDE), to tackle these high-dimensional data. Their key idea is to combine forecasts yielded by randomly generated “nondelay embeddings” of target variables. These “nondelay embeddings” can reconstruct the original state space for some cases and drastically reduce the possible number of embeddings. Ma et al.[10] showed that small embedding dimensions worked fine, even for high-dimensional dynamics, and successfully forecasted short-term high-dimensional data using the RDE framework. Ensembles tend to yield better results with significant diversity among its members[11,12], RDE only aggregates forecasts for a fixed embedding dimension with a fixed number of embeddings to combine, regardless of their forecast performance
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
