Developing two 4-parameter and 5-parameter exponential smoothing methods with multiplicative trend for demand forecasting

Exponential smoothing methods, especially Holt-Winters family, have been extensively utilized to demand time series forecasting. Previous studies show that Extended Holt Winters methods, by adding a smoothing constant to the level equation of Holt Winters methods, can improve the forecasting performance significantly. The improvements gained by the Extended Holt Winters method with additive trend motivated this research to extend this idea to the Holt Winters method with multiplicative trends too. In this paper, adding a smoothing constant to the Holt-Winters with multiplicative trend and also Holt-Winters with damped multiplicative trend was investigated, and the performance of these methods was compared with the classical methods. Quarterly and monthly time series of M3-Competition with the minimum length of ten years were used to measure the performance of proposed methods. The results showed that the proposed methods, significantly outperformed the classical Holt Winters multiplicative trend methods.