Averaging Methods of ForecastingDr. Ron Lembke

All-Time AverageTo forecast next period, take the average of

all previous periods

Advantages: Simple to use

Disadvantages: Ends up with a lot of dataGives equal importance to very old data

4/7/2009

Opening day

2010 Farm Angels:Ty 1.000 (first 6 at-bats)

MLB-Long-Run More Representative

Best season-ending (or to date) averages, active MLB playersMLB nothing changes over time. We want increasing sales2010 Farm Angels: Noah 0.823, Ty 0.767, Aidan 0.531

Moving AverageCompute forecast using n most recent

periods

Jan Feb Mar Apr May Jun Jul

3 month Moving Avg:June forecast: FJun = (AMar + AApr + AMay)/3If no seasonality, freedom to choose nIf seasonality is N periods, must use N, 2N,

3N etc. number of periods

Moving AverageAdvantages:

▫ Ignores data that is “too” old▫ Requires less data than simple average▫ More responsive than simple average

Disadvantages:▫ Still lacks behind trend like simple average,

(though not as badly)▫ The larger n is, more smoothing, but the

more it will lag▫ The smaller n is, the more over-reaction

Simple and Moving Averages

Period Demand All-Time 3MA1 102 12 103 14 11.04 15 12.0 12.05 16 12.8 13.76 17 13.4 15.07 19 14.0 16.08 21 14.7 17.39 23 15.5 19.0

10 16.3 21.0

Centered MA•CMA smoothes out

variability•Plot the average of 5

periods: 2 previous, the current, and the next two

•Obviously, this is only in hindsight

•FRB Dalls graphs

Centered Moving Average• Take average of n periods,• Plot the average in the middle period• Not useful for forecasting• More stable than actuals• If seasonality, n = season length (4wks, 12 mo, etc.)

CMA - # Periods to Average•What if data has 12-month cycle?

Ja F M Ap My Jn Jl Au S O N D Ja F M Avg of Jan-Dec gives average of month 6.5: (1+2+3+4+5+6+7+8+9+10+11+12)/12=6.5Avg of Feb-Jan gives average of month 6.5: (2+3+4+5+6+7+8+9+10+11+12+13)/12=7.5How get a July average? Average of other two averages

Stability vs. Responsiveness•Responsive

▫Real-time accuracy▫Market conditions

•Stable▫Forecasts being used throughout the

company▫Long-term decisions based on forecasts▫Don’t whipsaw those folks

Old DataComparison of simple, moving averages

clearly shows that getting rid of old data makes forecast respond to trends faster

Moving average still lags the trend, but it suggests to us we give newer data more weight, older data less weight.

Weighted Moving AverageFJun = (AMar + AApr + AMay)/3

= (3AMar + 3AApr + 3AMay)/9Why not consider:FJun = (2AMar + 3AApr + 4AMay)/9FJun = 2/9 AMar + 3/9 AApr + 4/9 AMay

Ft = w1At-3 + w2At-2 + w3At-1

Complicated:• Have to decide number of periods, and weights for each• Weights have to add up to 1.0• Most recent probably most relevant, gets most weight• Carry around n periods of data to make new forecast

Weighted Moving Average Period Demand 3WMA

1 102 123 144 15 12.65 16 14.16 17 15.37 19 16.38 21 17.89 23 19.6

10 21.6

Wts = 0.5, 0.3, 0.2F4= 0.5*14+ 0.3*12+ 0.2*10 = 12.6

Setting Parameters•Weighted Moving Average

▫Number of Periods▫Individual weights

•Trial and Error▫Evaluate performance of forecast based on

some metric

Exponential Smoothing

At-1 Actual demand in period t-1 Ft-1 Forecast for period t-1Smoothing constant >0, <1Forecast is old forecast plus a portion of the

error of the last forecast.Formulas are equivalent, give same answer

111 tttt FAFF F10 = F9 + 0.2 (A9 - F9)

111 ttt AFF F10 = 0.8 F9 + 0.2 (A9 - F9)

Exponential Smoothing•Smoothing Constant between 0.1-0.3•Easier to compute than moving average•Most widely used forecasting method,

because of its easy use•F1 = 1,050, = 0.05, A1 = 1,000•F2 = F1 + (A1 - F1) •= 1,050 + 0.05(1,000 – 1,050)•= 1,050 + 0.05(-50) = 1,047.5 units•BTW, we have to make a starting forecast

to get started. Often, use actual A1

Exponential Smoothing Period Demand ES

1 10 10.02 12 10.03 14 10.64 15 11.65 16 12.66 17 13.67 19 14.78 21 16.09 23 17.5

10 19.1

Alpha = 0.3

Exponential Smoothing Period Demand ES

1 10 10.02 12 10.03 14 11.04 15 12.55 16 13.86 17 14.97 19 15.98 21 17.59 23 19.2

10 21.1

Alpha = 0.5

Exponential SmoothingWe substitute the formula for F11 into F12, etc.Older demands get exponentially less weight

111112 1 FAF

101011 1 FAF

102

101112 11 FAAF

...1111 74

83

92

101112 AAAAAF

Choosing •Low : if demand is stable, we don’t want

to get thrown into a wild-goose chase, over-reacting to “trends” that are really just short-term variation▫ = 0 F10= F9= F8 – F never changes

•High : If demand really is changing rapidly, we want to react as quickly as possible

• = 1 F10= A9 – F is just the naïve – very responsive

111 tttt FAFF

Summary• All-Time average – too stable• Moving average – more responsive, still

lags the trend▫ Centered Moving average – just FYI

• Weighted Moving average▫ How many periods to use? Weights to be

set• Exponential Smoothing – most popular

▫ Easy to implement, one parameter to set