1. 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. 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. 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. 4 Training Data – Cumulative Sales for the First 39 Weeks T = 39

5. 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. 6 Time Series Autoregressive Moving Average Model: ARMA(1,1) – generally recognized to be a good approximation for many observed time series or

7. 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. 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. 9 Neural Networks (contd) AND Given the rule on the left, we deduce the pattern on the right:

10. 10 Neural Networks Structure of Neural Net Models:

11. 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. 12 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

13. 13 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)

14. 14 Probability Modeling After solving the integral, the cumulative probability function becomes: F(t) = LL = Estimation uses Excel Solver

15. 15

16. 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. 17 New Product Sales – Results T=39

18. 18 Time Series - Results Captures jumps in the training data Implies no additional sales (the product is dead), extreme case of forecast

19. 19 Neural Nets - Results Can sometimes be over-responsive to jumps in training data

20. 20 Probability Model - Results Overall, the best method Furthermore, allows the analyst to make statements about the consumers in the market

21. 21 Next Steps Include covariates Different training periods Perform comparative analysis for other areas of forecasting –Customer Lifetime Value

22. 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 www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/repo rt.html