Comparative Study of Sales Forecasting using LSTM and ARIMA Methods

Abstract

The current competitive manufacturing environment drives many companies to respond quickly to demand. One effective approach is to predict future market conditions. In this research, sales predictions were carried out using a case study of a lunch box manufacturing company. The company requires a method to predict lunch box sales to estimate the number of products to be produced. This aims to prevent excessive overproduction or underproduction. The prediction methods used in this research were Long Short-Term Memory (LSTM) and Autoregressive Integrated Moving Average (ARIMA). The LSTM method tends to be better suited to non-linear data such as market conditions, while ARIMA was used for comparison. Based on the prediction results for the company\'s two products, the LSTM method performed better than ARIMA in all assessment types: Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE), and Mean Squared Error (MSE).

Introduction

• In a fast-paced manufacturing environment, accurate sales forecasting is critical for inventory management, production planning, and financial decision-making.

• Traditional statistical models like ARIMA and modern deep learning models like LSTM are widely used for time-series forecasting.

• While ARIMA excels in capturing linear patterns, it struggles with the non-linear and chaotic nature of real-world sales data.

• LSTM (Long Short-Term Memory) networks are better suited to modeling complex, non-linear, and long-term dependencies in sequential data.

2. Literature Review

• Early forecasting models: Exponential smoothing, Moving Averages, ARIMA.

• ARIMA is based on the Box-Jenkins methodology with steps: model identification (p, d, q), parameter estimation, model validation, and forecasting.

• However, ARIMA struggles with non-linear patterns.

• LSTM, a type of RNN, overcomes the vanishing gradient problem and captures long-term dependencies using memory cells and gates (input, forget, output).

• LSTM is especially effective for complex sequences like sales data.

3. Methodology

• ARIMA Forecasting Steps:

  • Test for stationarity (ADF test).

  • Tune parameters (p, d, q) using combinations or ACF/PACF plots.

  • Split data into train, validation, and test.

  • Use the best parameters for forecasting and evaluate using:

    • MAD (Mean Absolute Deviation)

    • MAPE (Mean Absolute Percentage Error)

    • MSE (Mean Squared Error)

• LSTM Forecasting Steps:

  • Normalize data (MinMaxScaler).

  • Use a sliding window to create sequences.

  • LSTM model architecture:

    • Dense layers (64 and 32 neurons), dropout layer.

    • Optimizer: Adam, Loss: MSE, Epochs: 100.

  • Use multi-step prediction and evaluate with the same error metrics.

4. Case Study: Lunch Box Manufacturing Company

• Dataset: Monthly sales data (2020–2022) for two products:

  • 7200ml sealware

  • 3500ml sealware

ARIMA Results:

• Parameters:

  • 7200ml: (6,1,5)

  • 3500ml: (5,1,7)

• Average metrics:

  • MAD: 131.72

  • MAPE: 38.08%

  • MSE: 26,715.37

LSTM Results:

• Trained on the same dataset with a multi-step forecasting approach.

• Average metrics:

  • MAD: 76.55

  • MAPE: 21.26%

  • MSE: 10,470.13

Conclusion

This research predicted the sales of lunch boxes produced by a company using ARIMA and LSTM methods. The experiment was conducted using a dataset of sales data for two years. From the experimental results and measurements using MAD, MAPE, and MSE, it was shown that the prediction results using LSTM had better performance than the results using ARIMA. This shows that the LSTM method is more suitable for use on datasets for this case study because the lunch box sales data is non-linear.

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Copyright

Copyright © 2025 Rudy Adipranata, Leo Willyanto Santoso, Kenny Manuel Evan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.