Transcript Trend Adjusted Exponential Smoothing Forecast

T18-05 Trend Adjusted Exponential Smoothing Forecast
Purpose
Allows the analyst to create and analyze the "Trend
Adjusted Exponential Smoothing" forecast. The MAD
and MSE for the forecast are calculated, and a graphical
representation of history and forecast are shown.
Inputs
Historical Period Demand
Smoothing Constants (a and b)
Outputs
Trend Adjusted Exponential Smoothing Forecast
Forecast Error
MAD & MSE
Graph showing Historical Demand and Trend Adjusted
Exponential Smoothing Forecast
Limitations
60 Time Series Observations
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Time Series Techniques
Trend Adjusted Exponential Smoothing – forecast is projected based
on the trend of the historical data combined with exponential smoothing
Horizon: Short range
Method:
Ft +1  S t  Tt where S t = Smoothed Forecast,
Tt  current trend estimate, requires two smoothing
constants a , and b .
Strength: Ability to track changes in a linear trend
Weakness: Not very accurate when a longer forecasting
horizon is necessary, lags actual demand.
Initial trend is estimated based on 4 starting points, and smoothing
constants are chosen through trial.
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Forecast Accuracy
Given that a forecast is rarely correct, the methodology you choose
should be the one which provides the least error from the actual
historical demand. Forecast error is defined as the difference between
actual historical demand and the forecast.
  Forecast Error  A t  Ft
where A t  Actual historical demand at time t
Ft  Forecast at time t
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Forecast Error
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2
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11
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0
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Monitoring the Forecast
There are two measures used to monitor the accuracy of a forecast. The
Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE).
The MAD is the average of the absolute value of the forecast errors.
The MSE is the average of the squared forecast errors.
MAD  average abs( )

MSE  average ( )
2

Note: The formula for the MSE shown above may vary slightly. Some
textbooks divide the sum of the squared errors by n-1 rather than n.
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Trend Adjusted Exponential Smoothing Example
Week
1
2
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4
5
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History
700
724
720
728
740
742
758
750
770
775
Prepare a trend adjusted exponential
smoothing forecast with smoothing constants a
= .4 and b = .3.
Calculate the trend adjusted exponential
smoothing forecast, MAD and MSE.
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Input the History Values, and smoothing constants a and b
in the light green cells.
The Trend Adjusted
Exponential Forecast,
Error, MAD, and MSE are
automatically calculated.
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A graph showing the History Values and Trend Adjusted
Exponential Smoothing Forecast is automatically produced.
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