# Adjusted Exponential Smoothing by lff30040

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```									Adjusted Exponential Smoothing

Paul Mendenhall
BusM 361
Professor Foster
Outline
•   Tool defined
•   Equation Explained
•   Illustrated step by step problem
•   Practice Problem
•   Summary
Definition

• Times Series Forecasting model
• Adjusts for trends in information
Trends
• What are trends?
Long term movements in a time series.

• Why are trends a problem?
Cause lags in forecasts.
Smoothing and Alpha
• Alpha (α)
• If randomness is great than α is closer to 0.
– More weight on past data.
• If randomness is small than α is closer to 1.
– Greater weight on recent data.
Why the Model is Used

• Smoothes random information.
• Works with trends in information.
• Provides a more accurate forecast.
Equation

The equation is:

AFt+1 = F t+1 + Tt+1
Equation Explained
The equation is:    AFt+1 = F t+1 + Tt+1
where:

F t+1 = αDt + (1- α)Ft
T t+1 = β(F t+1 -Ft) + (1- β)Tt

Tt=1 = trend factor for the next
period.
Tt = trend factor for the current period
β = smoothing constant for the trend
Equation Illustrated
An electronics company is selling portable
CD players and estimated the demand for
the first period and forecasted the next three
The first periods demand is 50 players and
54 players was used to start the forecast.
β = 0.7 and α= 0.2 (see Table 1)
Equation Illustrated cont…
Period           Demand     Forecast Ft    Trend Tt   Forecast AFt

1               54         50              -          -

2               57          -              -          -

3               44          -              -          -

* α value is 0.2
** β value is 0.7

Table 1
Step 1
• Create a table in Excel and enter the figures for
the first period.
• Demand was 54.
• Unadjusted Forecast is any reasonable starting
figure to start the process, in this case 50 players.

Period   Demand       Forecast Ft   Trend Tt            AFt
1        54           50             -               -
Step 2
Calculate Ft+1 for period 2:
F t+1 = αDt + (1- α)Ft
F2 = 0.2*57+(1-0.2)*50 = 50.8

Period   Demand     Forecast Ft   Trend Tt            AFt
1        54         50             -               -
2        57        50.8            -               -
Step 3
Calculate the trend adjustment factor for period 2:
T t+1 = β(F t+1 -Ft) + (1- β)Tt
T2 = 0.7(50.8-50)+(1-0.7)*0 = 0.56

Period   Demand       Forecast Ft   Trend Tt            AFt
1        54           50             0               -
2        57          50.8          0.56              -
Step 4
AFt+1 = F t+1 + Tt+1
AF2 = 50.8 + 0.56 = 51.36

Period   Demand      Forecast Ft   Trend Tt            AFt
1        54          50             0               -
2        57         50.8          0.56            51.36
Complete the table
Now calculate the Adjusted Forecast for period 3.

Period   Demand      Forecast Ft   Trend Tt            AFt
1        54          50             0              50
2        57         50.8          0.56            51.36
3        44           -             -               -
Steps 1-4 Completed
• Now calculate the Adjusted Forecast for period 3.
• Forecast table completed.

Period   Demand      Forecast Ft   Trend Tt            AFt
1        54          50             0              50
2        57         50.8          0.56            51.36
3        44        52.04          1.036           53.08
Real World Example

Concise Co. is considering purchasing new equipment to
improve productivity, but must first do some financial
analysis. To provide accurate information for the analysis,
an accurate forecast of demand must be produced to
determine the estimated profit and cash flows for the next
year. Concise Co. is concerned about the accuracy of the
forecast due to dramatic movements is demand the last few
years. Top management has asked you, the financial
analysis, to create the forecasted report for 2005.
Real World Ex. Continued
You decide, after looking at the trends of the information,
that the adjusted exponential smoothing model would work
best for the forecast. Alpha is .3 and beta is .6. Use the
last five years to create next year’s forecasted demand…
Real World Ex. Continued
Top management has asked you, the financial analysis, to
create the forecasted report for 2005. Use the last five
years to create next year’s forecasted demand. The last
five years demand is provided in the graph below.

Year           Demand
2000            1376
2001            1189
2002            1122
2003            1306
2004            1213

Year     Demand     Forecast Ft   Trend Tt            AFt

2000      1376       1200            0             1200

2001      1189       1253           32             1284

2002      1122       1234            1             1235

2003      1306       1200           -20            1181

2004      1213       1232           11
Summary
•   Times series
•   Smoothing
•   Trends
•   Accurate forecasting