Sales%20Forecasting%20using%20Dynamic%20Bayesian%20Networks

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Sales Forecasting using Dynamic Bayesian
Networks

• Steve Djajasaputra
• SNN Nijmegen
• The Netherlands

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Table of Content

1. Why Sales Forecasting?
2. Method
3. Results Discussions
4. Conclusions
5. Further Research
6. Acknowledgements

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1. Why Sales Forecasting?

• Sales Forecasting bring advantage for your
  business
• reducing logistic cost
• improving your services
• targeted marketing
• lower backorder

But in practice is this really happening?
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The Answer is YES! An Example of Success Story

• Bayesian statistical technology for predicting
  newspaper sales
• 1 to 4 more sales with same deliveries
• 3 to 12 less deliveries to achieve same total
  amount of sales

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But time-series forecasting is not always easy!

• So.
• Searching better forecasting technology
• Aggregation of different group of products can be
  helpful
• Clustering methodology for aggregation
• Bayesian Methodology generative model

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2. Method

• Dynamic Bayesian Networks
• Forecasting
• The Inputs

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Dynamic Bayesian Networks

• Y is our observation
• e.g. sales of different products beer y1, beer
  y2,
• X-axis the time t (e.g.weeks)

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Dynamic Bayesian Networks

• In our model, we assume that our observation Y is
  generated with this dynamic
• X are inputs, for example sales of bier last
  week, weather information, prices, day labeling
• ? are hidden variables, which are
  unobserved/unknown
• ? is noise N(0,?2)

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Dynamic Bayesian Networks

• Hierarchical model
• Our hidden variables ? depend on other
  unobserved/unknown hidden variables M.

• Several ? from different product share the same
  M.
• A is a transition matrix for ?
• G is a transition matrix for M
• ? is noise N(0, ? )
• ? is noise N(0, ?M )

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Dynamic Bayesian Networks

• Inference Learning
• We have Y X data in our model
• But we dont know the values of hidden variables
  ?, M and their initial values
• We also dont know the correct value of
  parameters ?, ?M ,A,G and their initial values
• We solve these problems in Bayesian paradigm,
  using EM Algorithm.

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Forecasting

• Steps
• Training step find the model parameters and
  hidden variables ? 1T given the data from
  observation window X1T,Y1T, using EM algorithm
  and Kalman smoothing.
• Forecasting step predict ?Th and YTh h is
  the horizon of forecasting
• Updating step update the hidden variables ?1Th
  given the real value YTh
• Repeat the forecasting updating steps above in
  iterations.

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The Inputs

• By Autocorrelation FFT Spectrum analysis, for
  inputs (Xi,t) I decided to use
• Seasonality markers
• Recent sales (1 week ago)
• Last month sales (4 weeks ago)
• We need to keep the number of inputs as small as
  possible to avoid over-fitting.
• Since I consider seasonality recent sales, my
  model is somewhat comparable with SC model
  which is used by Pim Ouwehand.

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3. Results Discussions

• An Example of Result
• Residual Analysis
• Nonlinear Transformation
• The Offset Problem
• Removing Outliers
• Our Bayesian Approach vs Conventional Econometric
  Methods
• Need More Informative Inputs

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An Example of Result

• Mean Absolute Deviation (MAD) is 2346 beers
• Y-axis
• O is the real value
• X is the prediction
• X-axis weeks
• Training steps week 5..204
• Forecasting steps week 205..260, 1 week horizon
• This result is about the range of Winter method
  used by Pim Ouwehand.

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Residual Analysis

• To validate our model.
• Its showed that the residues (error) are noise
  as we assumed.
• Y predicted vs Error (figure on top)
• Error vs time (figure on bottom)
• Autocorrelation and FFT of Error
• Cross correlation Error vs Inputs

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Nonlinear Transformation

• To make data more linear gaussian since we
  assume our model is linear and the data is
  assumed to be gaussian distributed.
• e.g. Log, Sigmoid

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The Offset Problem

• Due to the stationary assumption, the software
  gives over(under)estimated forecasting if the
  trend is exist.
• Solutions
• Removing trend (e.g. taking difference)
• Updating the parameters after forecasting step.
• Legend
• Left moving averaged Beer-2 vs weeks
• Right Predicted Beer-2 vs weeks

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Removing Outliers

• The plot shows that the data is very noisy.
• Most of the outliers are below the mean, perhaps
  due to out of stock problem. Thus it will be
  helpful if we can get out of stock label for
  input in our forecasting model.

Sales of 10 beers (normalized) vs weeks
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Our Bayesian Approach vs Conventional Econometric
methods

• Econometric regression methods (e.g. Winter
  Method used by Pim Ouwehand) works well to fit
  the data.

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• However, we dont want just do fitting the data.
  We want to understand the process behind the data
  that we observed (i.e. hidden/unobserved
  variables).
• We want to have a generative model of the beer
  buyers.
• This generative model helps you to understand the
  hidden process in the market. This is a
  valuable insight for business decision, e.g. by
  simulation.

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We need More Informative Inputs
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4. Conclusions

• This preliminary research (only with the sales
  data without other informative inputs) showed
  that the result is about in the range of Winter
  method.
• We need more informative input data for a better
  model.
• Hacking data (e.g. removing trend, nonlinear
  transformation) slightly improves the result. But
  this is not the main purpose of this research.

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Conclusions continued

• We are not only just fitting the data but
  constructing a generative model, which is useful
  for understanding business process behind the
  sales.
• This understanding help you to shape your
  strategy to achieve more profit.

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5. Further Research

• Clustering and Structural Learning
• Non stationary process
• Non linear model
• Approximations
• Variational
• Factorial
• Monte Carlo (MCMC)

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6. Acknowledgements

• Our sponsor STW
• Tom Heskes (KUN)
• Pim Ouwehand (TUE)
• Bart Bakker (Phillips, was in KUN)
• Data providers/ Business Partners Schuitema,
  Technie Unie, OPG.

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Appendix Clustering Insights

• On Observed data Y

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• On hidden variables
• 1,2seasonality
• 3last month
• 4last week