A Hybrid Forecasting Method Based on The Exponential Smoothing and Multiplicative Neuron Model Artificial Neural Network

Year 2025, Volume: 9 Issue: 2, 37 - 43, 30.09.2025

Saime Şule Aksakal , Erol Eğrioğlu

https://doi.org/10.34110/forecasting.1792231

https://izlik.org/JA46SX84TG

Abstract

Holt exponential smoothing method is an effective method for forecasting of non-seasonal time series.
In Holt method, moving average operator with exponential decay weights is used. Multiplicative
neuron model artificial neural network is a popular artificial neural network type and it has been also
successfully used for the aim of forecasting of non-seasonal time series. In this study, a hybrid
forecasting method that combines the properties of both Holt exponential smoothing method and
multiplicative neuron model artificial neural network is proposed. The parameters and combination
weights for Holt method and multiplicative neuron model are determined by particle swarm
optimization. The final forecasts and confidence intervals for forecasts are obtained by using random
subsampling bootstrap method. Moreover, hypothesis tests for combination weights are applied by
using bootstrap samples. The proposed method is applied to Dow-Jones Industrial average stock
exchange data sets between the years 2010 and 2012 and the forecasting performance of proposed
method is compared with other some other methods in the literature.

Keywords

Hybrid method , Holt’s method , Multiplicative neuron model , Particle swarm optimization , Subsampling bootstrap method , Forecasting.

References

• Brown, RG. (1959). Statistical forecasting for inventory control, New-York, McGraw-Hill. Holt, CC. (1957). Forecasting seasonal and trends by exponentially weighted moving averages, Office of Naval Research, Research Memorandum, No: 52. Winters, PR. (1960). Forecasting sales by exponentially weighted moving averages. Management Science 6: 324-242. Gooijer, J., Hyndman, R. (2006). 25 years of time series forecasting. International Journal of Forecasting 22: 443–473.
• Yadav, RN., Kalra, PK., John, J. (2007). Time series prediction with single multiplicative neuron model. Applied Soft Computing 7: 1157-1163.
• Tseng, FM., Yu, HC., Tzeng, GH. (2002). Combining neural network model with seasonal time series ARIMA model. Technological Forecasting&Social Change 69: 71-87.
• Zhang, G. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50: 159-175.
• BuHamra, S., Smaoui, N., Gabr, M. (2003). The Box-Jenkins analysis and neural networks: prediction and time series modeling. Applied Mathematical Modeling 27: 805-815.
• Ince, H., Traffalis, TB. (2005). A hybrid model for exchange rate prediction. Decisions Support Systems 42: 1054-1062.
• Aladag, CH., Egrioglu, E., Kadilar, C. (2009). Forecasting nonlinear time series with a hybrid methodology. Applied Mathematic Letters 22: 1467-1470.
• Khashei, M., Bijari, M. (2012). A new class of hybrid models for time series forecasting. Expert Systems with Applications 39: 4344-4357.
• Lee, YS., Tong, LI. (2011). Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming. Knowledge-Based Systems 24: 66-72.
• Yolcu, U., Aladag, CH., Egrioglu, E. (2013). A new linear & nonlinear artificial neural network model for time series forecasting. Decision Support System Journals 54: 1340-1347.