Average

Report
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:
Ty 1.000 (first 6 at-bats)
MLB-Long-Run More Representative
Best season-ending (or to date) averages, active MLB players
MLB nothing changes over time. We want increasing sales
2010 Farm Angels: Noah 0.823, Ty 0.767, Aidan 0.531
Moving Average
Compute forecast using n most recent periods
Jan
Feb
Mar
Apr
May
Jun
Jul
3 month Moving Avg:
June forecast:
FJun = (AMar + AApr + AMay)/3
If no seasonality, freedom to choose n
If seasonality is N periods, must use N, 2N, 3N etc.
number of periods
Moving Average
Advantages:
▫
▫
▫
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
10
1
10
12
2
11.0
14
3
12.0
15
4
12.8
16
5
13.4
17
6
14.0
19
7
14.7
21
8
15.5
23
9
16.3
10
3MA
12.0
13.7
15.0
16.0
17.3
19.0
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
Avg of Jan-Dec gives average of month 6.5:
(1+2+3+4+5+6+7+8+9+10+11+12)/12=6.5
Avg of Feb-Jan gives average of month 6.5:
(2+3+4+5+6+7+8+9+10+11+12+13)/12=7.5
How get a July average? Average of other two averages
M
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 Data
Comparison 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 Average
FJun = (AMar + AApr + AMay)/3
= (3AMar + 3AApr + 3AMay)/9
Why not consider:
FJun
= (2AMar + 3AApr + 4AMay)/9
FJun = 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
10
2
12
3
14
4
15
12.6
5
16
14.1
6
17
15.3
7
19
16.3
8
21
17.8
9
23
19.6
10
21.6
Wts = 0.5, 0.3, 0.2
F4= 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
Ft  Ft 1    At 1  Ft 1 
F10 = F9 + 0.2 (A9 - F9)
Ft  1   Ft 1   At 1
F10 = 0.8 F9 + 0.2 (A9 - F9)
At-1 Actual demand in period t-1
Ft-1 Forecast for period t-1

Smoothing constant >0, <1
Forecast is old forecast plus a portion of the
error of the last forecast.
Formulas are equivalent, give same answer
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
1
10
2
12
3
14
4
15
5
16
6
17
7
19
8
21
9
23
10
Alpha = 0.3
ES
10.0
10.0
10.6
11.6
12.6
13.6
14.7
16.0
17.5
19.1
Exponential Smoothing
Period Demand
1
10
2
12
3
14
4
15
5
16
6
17
7
19
8
21
9
23
10
Alpha = 0.5
ES
10.0
10.0
11.0
12.5
13.8
14.9
15.9
17.5
19.2
21.1
Exponential Smoothing
We substitute the formula for F11 into F12, etc.
Older demands get exponentially less weight
F12   A11  1   F11
F11   A10  1   F10
F12   A11   1   A10  1    F10
2
F12   A11   1   A10   1    A9   1    A8   1    A7  ...
2
3
4
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
Ft  Ft 1    At 1  Ft 1 
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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