On the Approximation Capabilities of Deep Neural Networks for Multivariate Time Series: A Case Study on AAPL Stock Prices

Mohammad, Jamhuri, Mohammad Isa, Irawan, Ari, Kusumustuti, Kartick Chandra, Mondal and Juhari, Juhari (2025) On the Approximation Capabilities of Deep Neural Networks for Multivariate Time Series: A Case Study on AAPL Stock Prices. Cauchy: Jurnal Matematika Murni dan Aplikasi, 10 (2). pp. 1401-1416. ISSN 2477-3344

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Abstract

Multivariate time series forecasting plays a crucial role in various domains, including finance, where accurate stock price prediction supports strategic decision-making. Traditional methods such as Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), and Vector Autoregression (VAR) often fall short when dealing with complex, non-linear data—particularly those exhibiting long-term temporal dependencies. This study evaluates deep learning approaches, namely Multilayer Perceptron (MLP), Convolutional Neural Networks (CNN), and Long Short-Term Memory (LSTM), using daily AAPL stock price data from January 2020 to November 2024. The results show that the MLP model with a 10-day time window achieves the best accuracy, yielding lower values in Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) compared to CNN, LSTM, and VAR. The findings suggest that MLP is particularly effective in capturing complex patterns in multivariate time series forecasting.

Item Type:	Journal Article
Keywords:	Time series forecasting; temporal dependency; non-linear modeling; artificial neural networks; multivariate prediction
Subjects:	01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics 01 MATHEMATICAL SCIENCES > 0104 Statistics 01 MATHEMATICAL SCIENCES > 0199 Other Mathematical Sciences
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Juhari Juhari
Date Deposited:	09 Jul 2026 14:54

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