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

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

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:

Neural Networks

Structure of Neural Net Models:

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)

Probability Modeling

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

Results

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

New Product Sales - Results