Section 7.2: Exponential Smoothing

Quantitative Decision Making 7th edBy Lapin and Whisler

Simple Exponential Smoothing

Year t Yt Ft

2000 1 2014 -------2001 2 1648 20142002 3 1694 19042003 4 2115 18412004 5 2167 19232005 6 2410 19962006 7 2464 21202007 8 2145 22232008 9 1210 22002009 10 270 -------

tt1t F)1(YF

2.19042014*7.1648*3.

Graphing Actual vs Forecast ValuesSummit County Sales Activities

0

500

1000

1500

2000

2500

3000

Nu

mb

er

of

Sa

les

Time

Acutal Sales Forecasted Sales

Forecasting Errors

n

ttt FY

nMAD

1

1

n

t t

tt

YFY

nMAPE

1

100

2

1

)(1t

n

tt FY

nMSE

Two Parameter Smoothing

)bT)(1(YT 1t1ttt

1t1ttt b)1()TT(b

tt1t bTF

Simple Exponential Smoothing

Year t Yt Tt bt Ft

2000 1 2014 ------- -------- -------

2001 2 1648 2014 1648-2014

-366-------

2002 3 1694 2014-366

1648

2003 4 2115

Compute T3

1661)3662014(7.1694*3.

)bT(7.Y3.T 2233

Year t Yt Tt bt Ft

2000 1 2014 ------- -------- -------2001 2 1648 2014 -366 -------

2002 3 1694 1661 16482003 4 2115

Compute b3

363)366(*8.)20141661(2.

b)1()TT(b 2233

Year t Yt Tt bt Ft

2000 1 2014 ------- -------- -------

2001 2 1648 2014 -366 -------

2002 3 1694 1661 -363 1648

2003 4 2115

Seasonal Exponential Smoothing with Three Parameters Many time series have regular seasonal patterns to

be incorporated into forecasts. The three-parameter model incorporates a

seasonal smoothing constant (beta):

Tt = Yt /St –p) + (1 – )(Tt –1 + bt –1)

bt = (Tt – Tt –1) + (1 – )bt –1

St = Yt /Tt) + (1 – )St –p

Ft+1 = (Tt + bt) St –p+1

Forecasting withThree Parameters

Forecasting withThree Parameters The above works for p = 4 quarters or p =

12 months. The preceding slide needs 6 quarters to

generate the first (very bad) forecast. The process settles quickly, providing

good forecasts p periods into the future.