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