AUTOENCODER NEURAL NETWORK FOR UNIVARIATE TIME SERIES EMBEDDING
DOI:
https://doi.org/10.34185/1991-7848.itmm.2024.01.048Keywords:
time series analysis, time series embedding, dimensionality reduction, autoencoder, neural network, time series modeling, Takens’s theorem.Abstract
The problem of time series embedding is a universal one. It is the main prerequisite when it comes to modeling of dynamical processes using systems of autonomous ordinary differential equations (ODEs) because they have hard requirements for the dimensionality of the problem. One-dimensional ODE can only exhibit 3 types of behavior while two-dimensional ODE can exhibit 9. This is why it is important to increase the dimensionality of the problem before starting the modeling to allow for wider range of possible behaviors in the final model. One way to increase the dimensionality is to delay-embed the time series data but this approach can be extended to allow the use of an autoencoder neural network that would associate a higher-dimensional vector to each point in the time series and will allow the modeling to be performed in higher dimension.
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