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Averaging Methods of Forecasting. Dr. Ron Lembke. All-Time Average. To forecast next period, take the average of all previous periods Advantages: Simple to use Disadvantages: Ends up with a lot of data Gives equal importance to very old data. 4/7/2009 Opening day. 2010 Farm Angels : - PowerPoint PPT Presentation
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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
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