On the Approximation Capabilities of Deep Neural Networks for Multivariate Time Series Modeling

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.