Time Series Analysis with Exponential Smoothing and Grey GM(1,1) Models

Time Series Forecasting Using Exponential Smoothing Methods, Grey GM(1,1) Models, and Enhanced Approaches with Optimal Weighted Combination and Empirical Weighted Combination Models

Exponential Smoothing Method

Exponential Smoothing is one of the commonly used methods for time series forecasting, based on the theoretical foundation of trend extrapolation. It assumes that quantitative evolution characteristics of phenomena within a certain future period will not deviate from past development trends. The forecast value is a weighted sum of all previous observations, with different weights assigned to different data points - more recent data receives higher weights while older data receives lower weights. This method can be implemented using recursive formulas where the smoothing parameter α controls the weight decay rate.