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Trend adjusted exponential smoothing forecasting metho ds
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TREND ADJUSTED EXPONENTIAL SMOOTHING FORECASTING
METHOD
Quantitative Techniques in Decision Making
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)
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 = forecast for next period
Dt = actual value for present period
Ft = previously determined forecast for present period
α = weighting factor (between 0 and 1)
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
Adjusted Exponential Smoothing:
AFt+1 = Ft+1 + Tt+1
Where…
Tt +1 = β (Ft+1 – Ft ) + (1 - β ) Tt
= trend factor for the next period Tt = trend factor for the current period β = 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
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
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
Jan Feb Mar Apr May Jun Jul Aug Sep
Actual demand
Unadjusted forecast
Adjusted forecast
2200
2100
2000
1900
1800Hou
sing
sta
rts
Months
• 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)
Adjusted forecast (AFt)
in $
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
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