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 4th Annual Hawaii International Conference on Statistics, Mathematics, and Related Fields


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


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


Training Data - Cumulative Sales for the First 39 Weeks

JPG

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).


Time Series


* Autoregressive Moving Average Model: ARMA (1,1) - generally recognized to be a good approximation for many observed time series
JPG

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


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


Neural Networks (cont'd)


Given the rule on the left, we deduce the pattern on the right:
JPG

Neural Networks


Structure of Neural Net Models: JPG


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


Probability Modeling


* Probability models:
- Are representations of individual buying behavior
- Provide structural insight into the ways in which consumers make purchase decisions (Massy el at 1970)
* Specific assumptions of purchase process and latent propensity (Bayesian flavor)
* Explicit consideration of unobserved heterogeneity


Probability Modeling


* 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, a)
JPG


Probability Modeling


* After solving the integral, the cumulative probability function becomes: JPG * Estimation uses Excel Solver


JPG


Results


* All three models do a relatively good job predicting future sales, but Exponential Gamma is the best



JPG


New Product Sales - Results

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Time Series - Results


  • Captures jumps in the training data
  • Implies no additional sales (the product is dead), extreme case of forecast
JPG

Neural Nets - Results


  • Can sometimes be over-responsive to jumps in training data
JPG

Probability Model -Results


  • Overall, the best method
  • Furthermore, allows the analyst to make statements about the consumers in the market
JPG


Next Steps


  • Include covariates
  • Different training periods
  • Perform comparative analysis for other areas of forecasting
  • Customer Lifetime Value


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: 391410
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/report.html