This document describes the trend adjusted exponential smoothing forecasting method. It is a quantitative time series forecasting technique that calculates the weighted average of the current actual value and previous forecast, with an adjustment made for any trend present in the data. The trend adjustment is calculated using a smoothing constant and prior trend value. The method is preferred when a trend or seasonal pattern is evident in historical data. An example is provided to illustrate how to compute forecasts using this method by calculating the unadjusted forecast, trend, and adjusted forecast over multiple time periods.

1. Quantitative Techniques in
Decision Making
TREND ADJUSTED
EXPONENTIAL SMOOTHING
FORECASTING METHOD

2. Defining the Method
A Forecasting Model:
• Predicts future levels of a variable
• Can be either quantitative or qualitative
There are two types of quantitative models: Time series and Causal.
• Time series models see the future level of a variable as a function of
time. (exponential smoothing, weighted moving average models)
• Causal models, on the other hand, see the future level of a variable as a
function of something other than time. (regression models)

3. Exponential Smoothing
• Quantitative forecasting method
• Most widely practiced method of time series forecasting
• Weighted average of two variables
Ft+1 = α Dt + (1 – α )Ft
Where…
Ft +1 =
Dt =
Ft =
α =
forecast for next period
actual value for present period
previously determined forecast for
present period
weighting factor (between 0 and 1)

4. Adjusted Exponential Smoothing
Forecasting Method
• A method that uses measurable, historical data
observations, to make forecasts by calculating the
weighted average of the current period’s actual value
and forecast, with a trend adjustment added in.
When to Use the Method
• Preferred Scenario:
– When a trend is present
• Good Scenario:
– When there’s a cyclical or seasonal pattern

5. Adjusted Exponential Smoothing:
Where…
Tt +1 =
=
Tt =
β =
AFt+1 = Ft+1 + Tt+1
β (Ft+1 – Ft ) + (1 - β ) Tt
trend factor for the next period
trend factor for the current period
smoothing constant for the adjustment factor
(just add a trend adjustment factor)
Points to Consider:
• To start, pick an unadjusted forecast
• In period 1, trend equals 0

6. Problem: 2005 U.S. Housing Starts (monthly)
Given the following data for 9 months, compute trend adjusted
smoothing average. Use α = 0.3 (weighting factor),
β = 0.6 (smoothing constant for the trend adjustment factor)
Period
Month
Actual
Demand
Unadjusted
forecast
Trend
Adjusted
forecast
1
Jan
2188
2100
0
2
Feb
2228
2126
16
2142
3
Mar
1833
2157
25
2182
4
Apr
2027
2060
-48
2011
5
May
2041
2050
-25
2025
6
Jun
2065
2047
-12
2036
7
Jul
2062
2053
-1
2051
8
Aug
2038
2055
1
2056
9
Sep
2108
2050
-3
2047

7. Calculations:
Feb : unadjusted forecast:
Ft+1 = α Dt + (1 – α )Ft
= 0.3*2188 + 0.7*2100
= 2126
Trend factor for the next period:
Tt +1 =
β(Ft+1 – Ft ) + (1 - β)Tt
=
0.6*(2126 – 2100) – 0.4*0
=
16
Trend Adjusted Exponential Smoothing:
AFt+1 = Ft+1 + Tt+1
= 2126 + 16
= 2142

8. Housing starts
2200
Actual demand
Unadjusted forecast
2100
Adjusted forecast
2000
1900
1800
Jan
Feb
Mar
Apr
May
Jun
Months
Jul
Aug
Sep

9. • Problem :2 Intel quarterly sales revenue.
Given the following data for 4 months, compute trend
adjusted smoothing average. Use α = 0.3 (weighting factor),
β = 0.6 (smoothing constant for the trend adjustment factor)
Quarter
Month
ending
Sales
revenue
(actual) in $
Unadjusted
forecast(α=o.4)
in $
Trend
(β=0.7)
1
Dec-04
110,448
105,000
0
2
Mar-05
105,707
3
Jun-05
115,552
4
Sep-05
111,396
5
Dec-05
Adjusted
forecast (AFt)
in $

10. Solution
Quarter
Month
ending
Sales
revenue
(actual) in $
Unadjusted
forecast(α=o.4)
in $
Trend
(β=0.7)
in $
Adjusted
forecast (AFt)
in $
1
Dec-04
110,448
105,000
0
2
Mar-05
105,707
107,179
1525
108,705
3
Jun-05
115,552
106,590
45
106,636
4
Sep-05
111,396
110,175
2523
112,698
5
Dec-05
110,663
1099
111,762