New Forecast= Last period’s forecast + a (last period’s actual demand) – last period’s forecast)
a – weight or smoothing constant value between 0 and 1,
Ft = Ft-1 + a (At-1 – Ft-1)
Ft – New focecast,
Ft-1 – previous period’s forecast,
a = smoothing (or weighting) constant (0= a=1)
At-1 = Previous Year’s Actual Demand
Smoothing constant
Most recent
II
III
IV
V
a = 0.1
0.1
0.09
0.081
0.073
0.066
a = 0.5
0.5
0.25
0.125
0.063
0.031
– High value of a is chosen when underlying average is likely to change.
– Low values of a is chosen when underlying average is likely to change.
Measuring Forecast Errors- overall accuracy of forecasting model- Moving Average, Exponential Smoothing- determined by comparing forecasted values with actual or observed values.
If Ft denotes forecast in period t, At denotes actual demand in period t, forecast error (or deviation) is defined as
Forecast Error = Actual Demand- Forecast Value = At-Ft
Mean Absolute Deviation (MAD) –
MAD = S( Actual-Forecast) / n
A measure of the overall forecast error for a model.
During the past 8 quarters, Part of ABC has unloaded large quantities of grain from ships. The part’s operations manager wants to test the use of exponential smoothing to see how well the technique works in predicting tonnage unloaded. He guesses that the forecast of grain unloaded in the first quarter was 175 tons. Two values of a are to be examined: a = 0.10 and a = 0.50
Compare the actual data with the data we forecast (using each of the two a values) and then find the absolute deviation and MADs.
To evaluate the accuracy if each smoothing constant, we can compute forecast errors in terms of absolute deviations and MADs.
Mean Squared Error –
Mean Squared Error – second way of measuring overall forecast error.
MSE = S (Forecast errors)2 / n
n
Mean Absolute Percent Error- MAPE= S 100 (¦Actual- Forecast i¦/ Actual ) / n
i=1
Ft = a (At-1) + (1-a) (Ft-1 + Tt-1)
Tt= ß (forecast this period – forecast last period) + (1-ß) (Trend estimate last period)
Tt = ß(Ft – Ft-1) + (1-ß) Tt-1
Ft – exponentially smoothed forecast of data series in period t,
Tt – exponentially smoothed trend in period t,
At- actual demand in period t
a – smoothing constant for average (0= a=1)
ß – smoothing constant for trend (0= a=1)
Step #1. Compute Ft exponentially smoothed forecast for period t, using eg. (3-9)
Step #2. Compute the smoothed trend, Tt, using eg. (3-10)
Step #3. Calculate forecast including trend, FITt, by formula FITt = Ft + Tt