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

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Presentation Transcript
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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
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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
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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

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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).

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

or

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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

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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

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Neural Networks (cont’d)

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

AND

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Neural Networks

Structure of Neural Net Models:

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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

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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

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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)

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

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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)

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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

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Neural Nets - Results
  • Can sometimes be over-responsive to “jumps” in training data

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

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

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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

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