1. Simple Exponential Smoothing The forecast value is a weighted average of all the available previous values The weights decline geometrically Gives more weight to recent observations.

2. α = smoothing constant The weight of the most recent observation is assigned by multiplying the observed value by α The next most recent observation is (1- α) α The next observation by (1- α) 2 α

3. Simple Exponential Smoothing The weighting factor is  Subjectively chosen Range from 0 to 1 Smaller  gives more smoothing, larger  gives less smoothing The weight is: Close to 0 for smoothing out unwanted cyclical and irregular components Close to 1 for forecasting (continued)

4. Exponential Smoothing Model Single exponential smoothing model where: F t+1 = forecast value for period t + 1 y t = actual value for period t F t = forecast value for period t  = alpha (smoothing constant) or:

5. Exponential Smoothing Example Suppose we use weight  =.2 Quarter (t) Sales (y t ) Forecast from prior period Forecast for next period (F t+1 ) 1 2 3 4 5 6 7 8 9 10 etc… 23 40 25 27 32 48 33 37 50 etc… NA 23 26.4 26.12 26.296 27.437 31.549 31.840 32.872 33.697 etc… 23 (.2)(40)+(.8)(23)=26.4 (.2)(25)+(.8)(26.4)=26.12 (.2)(27)+(.8)(26.12)=26.296 (.2)(32)+(.8)(26.296)=27.437 (.2)(48)+(.8)(27.437)=31.549 (.2)(33)+(.8)(31.549)=31.840 (.2)(37)+(.8)(31.840)=32.872 (.2)(37)+(.8)(32.872)=33.697 (.2)(50)+(.8)(33.697)=36.958 etc… F 1 = y 1 since no prior information exists

6. Sales vs. Smoothed Sales Seasonal fluctuations have been smoothed NOTE: the smoothed value in this case is generally a little low, since the trend is upward sloping and the weighting factor is only.2

7. good It requires a limited quantity of data It is simpler than other forecasting methods bad Its forecast lag behind the actual data It has no ability to adjust for any trend or seasonality in data

8. Exponential Smoothing in Excel Use: Data / data analysis / exponential smoothing The “damping factor” is (1 -  )