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Hypercomplex neural network in time series forecasting of stock data

Radosław Kycia, Agnieszka Niemczynowicz

TL;DR

The paper tackles time-series stock forecasting using multiple interrelated series by comparing CNN, RNN, and $4D$ hypercomplex neural networks. It systematically optimizes hyperparameters with grid search and cross-validation, and it investigates how the order of four input series affects learning and efficiency. The results show that hypercomplex dense layers achieve similar $MAE$ to conventional architectures while dramatically reducing trainable parameters, enabling faster training and inference. This highlights the practical potential of $4D$ hypercomplex networks for efficient, real-time time-series forecasting in constrained environments such as embedded systems.

Abstract

The goal of this paper is to test three classes of neural network (NN) architectures based on four-dimensional (4D) hypercomplex algebras for time series prediction. We evaluate different architectures, varying the input layers to include convolutional, Long Short-Term Memory (LSTM), or dense hypercomplex layers for 4D algebras. Four related Stock Market time series are used as input data, with the prediction focused on one of them. Hyperparameter optimization for each architecture class was conducted to compare the best-performing neural networks within each class. The results indicate that, in most cases, architectures with hypercomplex dense layers achieve similar Mean Absolute Error (MAE) accuracy compared to other architectures, but with significantly fewer trainable parameters. Consequently, hypercomplex neural networks demonstrate the ability to learn and process time series data faster than the other tested architectures. Additionally, it was found that the ordering of the input time series have a notable impact on effectiveness.

Hypercomplex neural network in time series forecasting of stock data

TL;DR

The paper tackles time-series stock forecasting using multiple interrelated series by comparing CNN, RNN, and hypercomplex neural networks. It systematically optimizes hyperparameters with grid search and cross-validation, and it investigates how the order of four input series affects learning and efficiency. The results show that hypercomplex dense layers achieve similar to conventional architectures while dramatically reducing trainable parameters, enabling faster training and inference. This highlights the practical potential of hypercomplex networks for efficient, real-time time-series forecasting in constrained environments such as embedded systems.

Abstract

The goal of this paper is to test three classes of neural network (NN) architectures based on four-dimensional (4D) hypercomplex algebras for time series prediction. We evaluate different architectures, varying the input layers to include convolutional, Long Short-Term Memory (LSTM), or dense hypercomplex layers for 4D algebras. Four related Stock Market time series are used as input data, with the prediction focused on one of them. Hyperparameter optimization for each architecture class was conducted to compare the best-performing neural networks within each class. The results indicate that, in most cases, architectures with hypercomplex dense layers achieve similar Mean Absolute Error (MAE) accuracy compared to other architectures, but with significantly fewer trainable parameters. Consequently, hypercomplex neural networks demonstrate the ability to learn and process time series data faster than the other tested architectures. Additionally, it was found that the ordering of the input time series have a notable impact on effectiveness.
Paper Structure (11 sections, 8 equations, 3 figures, 3 tables)

This paper contains 11 sections, 8 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. A brief review of deep learning time series forecasting approach
  3. Classical Convolutional Neural Networks
  4. Classical Recurrent Neural Networks
  5. Classical Long Short-Term Memory
  6. Four-dimensional hypercomplex neural networks
  7. Experimental setup
  8. Dataset
  9. Methodology
  10. Results
  11. Conclusions

Figures (3)

  • Figure 1: Architecture RNN. On the left, there is the classical RNN structure. On the right, there is the unfolding version where the information from the previous time step ($t-1$) is transformed to the next time step ($t$).
  • Figure 2: Selected stock prices in the period from January 1, 2015, to January 1, 2023. The ellipses marked notable correlations between values of given stock.
  • Figure 3: Testing architecture.