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Deep-learning model using hybrid adaptive trend estimated series for modelling and forecasting sales

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Abstract

Existing sales forecasting models are not comprehensive and flexible enough to consider dynamic changes and nonlinearities in sales time-series at the store and product levels. To capture different big data characteristics in sales forecasting data, such as seasonal and trend variations, this study develops a hybrid model combining adaptive trend estimated series (ATES) with a deep neural network model. ATES is first used to model seasonal effects and incorporate holiday, weekend, and marketing effects on sales. The deep neural network model is then proposed to model residuals by capturing complex high-level spatiotemporal features from the data. The proposed hybrid model is equipped with a feature-extraction component that automatically detects the patterns and trends in time-series, which makes the forecasting model robust against noise and time-series length. To validate the proposed hybrid model, a large volume of sales data is processed with a three-dimensional data model to effectively support business decisions at the product-specific store level. To demonstrate the effectiveness of the proposed model, a comparative analysis is performed with several state-of-the-art sales forecasting methods. Here, we show that the proposed hybrid model outperforms existing models for forecasting horizons ranging from one to 12 months.

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Notes

  1. https://www.kaggle.com/c/walmart-recruiting-store-sales-forecasting/data.

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Acknowledgements

This article was directed by Software Evaluation and Re-Engineering Research Lab (SERER Lab) and supported by the scientific research project of the Czech Sciences Foundation Grant No. 19-15498S.

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Authors and Affiliations

  1. Institute of Information Technology, Noakhali Science and Technology University, Noakhali, Bangladesh

    Md. Iftekharul Alam Efat, Rahat Uddin Azad, Md. Al Jaber & Shuvra Aditya

  2. Science and Research Centre, Faculty of Economics and Administration, University of Pardubice, Studentska 84, 53210, Pardubice, Czech Republic

    Petr Hajek

  3. Department of Finance, Performance and Marketing, Teesside University International Business School, Teesside University, Middlesbrough, Tees Valley, TS1 3BX, UK

    Mohammad Zoynul Abedin

  4. Department of Economics and Finance, University of New Orleans, New Orleans, LA, 70148, USA

    Mohammad Kabir Hassan

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Appendix 1: Forecasting error performance for the Walmart sales dataset

Appendix 1: Forecasting error performance for the Walmart sales dataset

Statistical time-series methods

Time dimension

ARIMA

HWES

PROPHET

SES

SARIMA

ATES

RMSE

One month

0.1072

0.1630

0.2135

0.1678

0.1147

0.0824

One quarter

0.2833

0.3345

0.3342

0.8877

0.2567

0.2100

Half year

0.3976

0.5782

0.4123

1.2340

0.4123

0.3321

One year

0.7560

0.8876

0.5678

1.3456

0.6318

0.4567

MAPE

One month

14.58%

18.96%

23.78%

17.90%

13.59%

8.62%

One quarter

18.56%

24.80%

25.23%

28.31%

21.93%

17.24%

Half year

26.79%

31.21%

28.35%

47.10%

25.02%

23.77%

One year

41.35%

44.87%

31.41%

55.42%

32.28%

27.66%

PFE

One Month

4.66%

4.99%

5.67%

4.96%

4.92%

4.23%

One quarter

8.56%

8.92%

9.22%

10.12%

8.26%

7.38%

Half year

11.23%

11.76%

11.22%

16.78%

11.42%

10.26%

One year

13.44%

13.77%

13.23%

20.03%

13.18%

11.23%

Neural network models

Time dimension

ANN

CNN

DNN

LSTM

GRU

CNN + LSTM

GRU–CNN–LSTM

RMSE

One month

0.2105

0.1194

0.1044

0.1223

0.1072

0.1361

0.0918

One quarter

0.3012

0.1988

0.2109

0.2467

0.2234

0.2123

0.1876

Half year

0.3987

0.3184

0.2908

0.3123

0.2987

0.2911

0.2843

One year

0.6881

0.4765

0.4908

0.5467

0.4654

0.4678

0.4123

MAPE

One month

24.58%

15.11%

13.23%

13.79%

14.17%

14.09%

12.11%

One quarter

30.21%

24.45%

23.78%

21.90%

19.54%

20.10%

17.00%

Half year

41.89%

31.22%

29.09%

33.89%

28.22%

29.21%

23.22%

One year

49.56%

41.22%

39.54%

40.22%

38.78%

39.22%

31.87%

PFE

One month

4.90%

4.60%

4.39%

4.12%

4.34%

4.31%

4.01%

One quarter

8.23%

8.37%

9.01%

8.47%

8.21%

8.01%

7.64%

Half year

11.23%

10.89%

10.18%

10.23%

10.01%

11.21%

9.87%

One year

13.78%

13.58%

13.15%

13.45%

12.69%

12.27%

11.78%

Hybrid time-series/neural network models

Time dimension

ATES + CNN

ATES + DNN

ATES + GRU

ATES + GRU–CNN–LSTM

RMSE

One month

0.1241

0.1356

0.1230

0.0851

One quarter

0.1723

0.1733

0.2145

0.1409

Half year

0.2562

0.2312

0.2876

0.2133

One year

0.3578

0.3289

0.3512

0.2809

MAPE

One month

16.12%

15.32%

14.93%

12.43%

One quarter

18.21%

18.81%

18.99%

16.22%

Half year

24.34%

26.22%

26.44%

22.65%

One year

30.18%

31.45%

30.70%

28.11%

PFE

One month

4.32%

4.12%

4.22%

2.43%

One quarter

7.88%

7.78%

7.65%

5.38%

Half year

10.83%

10.67%

10.27%

8.88%

One year

13.32%

12.51%

13.01%

11.32%

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Efat, M.I.A., Hajek, P., Abedin, M.Z. et al. Deep-learning model using hybrid adaptive trend estimated series for modelling and forecasting sales. Ann Oper Res 339, 297–328 (2024). https://doi.org/10.1007/s10479-022-04838-6

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