Parameter Optimization In Grey Holt – Winter Exponential Smoothing Using Golden Section

Abstract

Grey Holt-Winter Exponential Smoothing is a combination of Grey and exponential smoothing methods used to forecast seasonal trends and seasonal time series data with randomness, irregularity and limited data information that available. The parameter values for smoothing level (α), trend (β) and seasonal (γ) in the Grey Holt - Winter method affect the performance of the forecasting model. The Grey Holt - Winter Method has not yet provided a way to select the optimal value of the smoothing parameter to minimize the size value of the forecast error. In this research, the Golden Section method is used to obtain the optimal value of the smoothing parameter.

The Golden Section method has the basic concept of narrowing the interval of the origin area, so that the optimal value of the smoothing parameter is obtained in the Grey Holt-Winters forecasting. Mean Absolute Percentage Error (MAPE) is used to measure forecasting errors. The results of this research are comparison MAPE generated by the conventional method of Grey-Holt Winter Exponential Smoothing method with MAPE of Grey-Holt Winter Exponential Smoothing values using Golden Section parameter optimization. The data set used in this research is the Room Occupancy Rate of Star Hotel in Special Region of Yogyakarta from January 2008 - December 2017.

Based on the test result for the data testing in amount of 96, obtained a minimum forecasting error based on the conventional method of Grey Holt Winter Exponential Smoothing is 16.06%, while the forecasting error minimum produced by the Grey Holt Winter Exponential Smoothing method with the Golden Section is 13.92% with the optimal parameter value proposed is α equal to 0.146, β is 0.010 and γ is 0.146.