Comparing Time Series, Neural
Nets and Probability Models for
New Product Trial Forecasting
•
Eugene Brusilovskiy
•
Ka Lok Lee
•
These slides are based on the authors’
presentation at the 4
th
Annual Hawaii
International Conference on Statistics,
Mathematics, and Related Fields
2
Problem Introduction
•
Goal: To predict future sales using sales information from
an introductory period
•
Product: A new (unnamed) soft beverage that was
introduced to a test market
•
Data: We have 52 weeks of sales data, which we split into
training (first 39 weeks) and validation (last 13 weeks)
datasets
–
We build the models using the training dataset and
then examine how well the models predict sales in the
last 13 weeks
•
The methods employed here apply to predicting the sales
of any newly introduced consumer good
3
Prediction Methods Used
•
Time Series
–
Most common technique, available in almost every
statistics software
•
Neural Nets
–
Extensive data

mining tool (requires expensive
software)
•
Probability Modeling
–
Not always available in standard statistical packages,
may be coded in Excel
4
Training Data
–
Cumulative Sales for the First 39
Weeks
T = 39
5
Time Series
•
A
time

series
(TS)
model
accounts for patterns in the
past movements of a variable and uses that information
to predict its future movements. In a sense a time

series
model is just a sophisticated method of extrapolation
(Pindyck and Rubinfeld, 1998).
6
Time Series
•
Autoregressive Moving Average Model: ARMA(1,1)
–
generally recognized to be a good approximation for
many observed time series
or
7
Neural Networks
•
A
Neural Network
(NN)
is an information processing
paradigm inspired by the way the brain processes
information (Stergiou and Siganos, 1996).
•
MLP (The Multi

Layer Perceptron) is used here
8
Neural Networks
•
A Neural Network consists of neuron
layers
of 3 types:
–
Input
layer
–
Hidden
layer
–
Output
layer
•
We use two models with different MLP architectures: a
model with one hidden layer and a model with a skip
layer
9
Neural Networks (cont’d)
AND
Given the rule on the left, we deduce the pattern on the right:
10
Neural Networks
Structure of Neural Net Models:
11
Neural Networks
•
Neural Networks are especially useful for problems
where
–
Prediction is more important than explanation
–
There are lots of training data
–
No mathematical formula that relates inputs to
outputs is known
•
Source: SAS Enterprise Miner Reference Help.
Neural Network Node: Reference
12
Probability Modeling
•
Probability m
odels
:
–
Are representations of
individual
buying
behavior
–
Provide structural insight into the ways in which
consumers make purchase decisions (Massy el at.,1970)
•
Specific a
ssumption
s
of purchase process and latent
propensity
(Bayesian flavor)
•
Explicit consideration of unobserved heterogeneity
13
Probability Model
ing
•
Individual purchase time or time

to

trial is modeled by
“Diffusion Model”.
•
Exponential

Gamma
(EG)
, also known as
the
Pareto
distribution
(Hardie et al., 2003)
•
Time to trial ~
Exponential
(
λ
)
•
λ
~ Gamma (r,
α
)
14
Probability Model
ing
•
After solving the integral, the cumulative probability
function becomes:
•
F(t) =
•
LL =
•
Estimation uses Excel Solver
15
16
Results
Exp.
Gamma
Neural
Nets
Time
Series
Mean Absolute
Percentage Error
(MAPE)
2.7%
9.0%
5.5%
Where T is the total number of time periods (weeks). Here, t=1 is the
first validation week (week 40)
•
All three models do a relatively good job predicting future
sales, but Exponential Gamma is the best
17
New Product Sales
–
Results
T=39
18
Time Series

Results
•
Captures “jumps” in the training data
•
Implies no additional sales (the product is “dead”),
extreme case of forecast
19
Neural Nets

Results
•
Can sometimes be over

responsive to “jumps” in training
data
20
Probability Model

Results
•
Overall, the best method
•
Furthermore, allows the analyst to make statements
about the consumers in the market
21
Next Steps
•
Include covariates
•
Different training periods
•
Perform comparative analysis for other areas of
forecasting
–
Customer Lifetime Value
22
References
•
Hardie B. G.S., Zeithammer R., and Fader P. (2003),
Forecasting New Product Trial in a Controlled Test
Market Environment,
Journal of Forecasting,
22: 391

410
•
Massy, W.F., Montgomery, D.B. and Morrison, D.G.
(1970),
Stochastic Models of Buying Behavior
, The M.I.T.
Press, 464 pp.
•
Pindyck, R.S. and Rubinfeld D.L. (1998),
Econometric
Models and Economic Forecasts
, Irwin/McGraw

Hill.
•
SAS Enterprise Miner Reference Help. Article:
Neural
Network Node: Reference
•
Stergiou, C., & Siganos, D. (1996), Introduction to Neural
Networks. Available online at
www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/repo
rt.html
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