3. Forecasting
Marketing: forecasts sales for new and
existing products.
Production: uses sales forecasts to plan
production and operations; sometimes
involved in generating sales forecasts.
4. Characteristics of Forecasts
They are usually wrong
A good forecast is usually more than a
single number
Aggregate forecast are more accurate
The longer the forecasting horizon, the
less accurate the forecasts will be
Forecasts should not be used to the
exclusion of known information
5. Forecasting Horizon
Short term
(inventory management, production plans..)
Intermediate term
(sales patterns for product families..)
Long term
(long term planning of capacity needs)
7. Types of forecasting Methods
Subjective methods
Sales force composites
Customer survey
Jury of executive opinion
The Delphi method
Objective methods
Causal methods
Time series methods
8. Qualitative Methods
Don’t have data
Don’t have time to develop a forecast
Often used in practice
“Close enough”
Depend on expert opinions
Market surveys
More appropriate for long term forecasts
9. Delphi Technique
A method to obtain a consensus forecast
by using opinions from a group of
“experts”
expert opinion
consulting salespersons
consulting consumers
10. Causal Methods
Causal methods use data from sources other than the
series being predicted.
If Y is the phenomenon to be forecast and X1 , X2 , . .., Xn are
the n variables we believe to be related to Y, then a causal
model is one in which the forecast for Y is some function of
these variables:
Y = f (X1 , X2 , . .., Xn )
Econometric models are causal models in which the
relationship between Y and (X1 , X2 , . .., Xn ) is linear.
That is
Y = ao + a1 X1 + a2 X2 + … an Xn
for some constants a1 , a2 , . . . , an
11. Forecasting Steps for
Quantitative Methods
Collect data
Reduce/clean data
Build and evaluate model(s)
Forecast (model extrapolation)
Track the forecast
12. Identify the correct pattern
• Collect data. Look for possible cause/effect
relationships
• Determine which form can be used to
generate the pattern
• Determine specific values of the parameters
14. Building Models
Plot data over time. (remove outliers & get right
scale).
Using part of the data, estimate model parameters.
Forecast the rest of the data with the model.
Evaluate accuracy of the model.
Use judgment to modify.
Keep track of model accuracy over time (redo, if
needed).
18. Notation
: Observed value of the demand during period t
time series we would like to predict
forecast made for period t in period t-1
forecast made at the end of t-1 after having
observed , , …1−tD
:
:}1,{
t
t
t
F
tD
D
≥
2−tD
23. TIME SERIES METHODS
Stationary Series
A stationary time series is represented by a
constant plus a random fluctuation:
Dt = µ+ εt
where µ is an unknown constant corresponding to
the mean of the series and εt is a random error
with mean 0 and variance σ2
.
The methods described for stationary series are:
Moving Averages
Exponential Smoothing
24. Methods of Forecasting
Stationary Series
Moving Averages
Exponential Smoothing
N
DDD
N
D
F Nttt
t
Nti
i
t
−−−
−
−= +++
==
∑ ...21
1
11 )1( −− −+= ttt FDF αα
26. Month Deliveries
Jan 120
Feb 90
Mar 100
Apr 75
May 110
Jun 50
Jul 75
Aug 130
Sep 110
Oct 90
0
20
40
60
80
100
120
140
Jan Feb Mar Apr May Jun Jul Aug Sep Oct
Mont h
27. Month Deliveries MA(3) MA(6)
Jan 120
Feb 90
Mar 100
Apr 75 103
May 110 88
Jun 50 95
Jul 75 78 91
Aug 130 78 83
Sep 110 85 90
Oct 90 105 92
110 94
31. EXPONENTIAL SMOOTHING
Current forecast is a weighted average of the
last forecast and the current value of demand
New forecast = α (current observation of demand)
+ (1- α ) (last forecast)
38. Smaller values of α produce more stable forecasts,
whereas larger values of α will produce forecasts
which react more quickly to changes in the demand
pattern.
40. Similarities & Differences
Stationary series
Single parameter
Lag behind a trend
When α=2/(N+1)
Same distribution of
forecast error
ES weighted average
of all past data
MA only last N periods
MA : save past N data
ES : only last forecast