Exponential Smoothing Methods 1 Chapter Topics Introduction to exponential smoothing Simple Exponential Smoothing Holt’s Trend Corrected Exponential Smoothing Holt-Winters Methods Multiplicative Holt-Winters method Additive Holt-Winters method Slide 2 Motivation of Exponential Smoothing Simple moving average method assigns equal weights (1/k) to all k data points. Arguably, recent observations provide more relevant information than do observations in the past. So we want a weighting scheme that assigns decreasing weights to the more distant observations. Slide 3 Exponential Smoothing Exponential smoothing methods give larger weights to more recent observations, and the weights decrease exponentially as the observations become more distant. These methods are most effective when the parameters describing the time series are changing SLOWLY over time. Slide 4 Data vs Methods No trend or seasonal pattern? Y Single Exponential Smoothing Method N Linear trend and no seasonal pattern? Y Holt’s Trend Corrected Exponential Smoothing Method N Both trend and seasonal pattern? N Y Holt-Winters Methods Use Other Methods Slide 5 Simple Exponential Smoothing The Simple Exponential Smoothing method is used for forecasting a time series when there is no trend or seasonal pattern, but the mean (or level) of the time series yt is slowly changing over time. NO TREND model yt   o   t Slide 6 Procedures of Simple Exponential Smoothing Method Step 1: Compute the initial estimate of the mean (or level)n of the series at time period t = 0 yt  0  y  t 1 n Step 2: Compute the updated estimate by using the smoothing equation T  yT  (1   )T  1 where  is a smoothing constant between 0 and 1. Slide 7 Procedures of Simple Exponential Smoothing Method Note that T  yT  (1   )T  1  yT  (1   )[ yT  1  (1   )T  2 ]  yT  (1   ) yT  1  (1   ) 2 T  2  yT  (1   ) yT  1  (1   ) 2  yT 