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Comparing Time Series, Neural Nets and Probability Models for New Product Trial Forecasting

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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

3

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).

5

Time Series

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

or

6

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

7

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

8

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

11

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 assumptionsof purchase process and latent propensity (Bayesian flavor)
- Explicit consideration of unobserved heterogeneity

12

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, α)

13

Probability Modeling

- After solving the integral, the cumulative probability function becomes:
- F(t) =
- LL =
- Estimation uses Excel Solver

14

Results

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

Where T is the total number of time periods (weeks). Here, t=1 is the first validation week (week 40)

16

Time Series - Results

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

18

Probability Model - Results

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

20

Next Steps

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

21

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/report.html

22

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