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Sales Forecasting using Dynamic Bayesian Networks

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Sales Forecasting using Dynamic Bayesian Networks

Steve Djajasaputra

SNN Nijmegen

The Netherlands

- Why Sales Forecasting?
- Method
- Results & Discussions
- Conclusions
- Further Research
- Acknowledgements

Steve Djajasaputra (SNN Nijmegen)

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

But in practice… is this really happening?

Steve Djajasaputra (SNN Nijmegen)

- 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

Steve Djajasaputra (SNN Nijmegen)

So….

- Searching betterforecasting technology
- Aggregation of different group of products can be helpful
- Clustering methodology for aggregation
- Bayesian Methodology: generative model

Steve Djajasaputra (SNN Nijmegen)

- Dynamic Bayesian Networks
- Forecasting
- The Inputs

Steve Djajasaputra (SNN Nijmegen)

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

Steve Djajasaputra (SNN Nijmegen)

- 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)

Steve Djajasaputra (SNN Nijmegen)

- 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 )

Steve Djajasaputra (SNN Nijmegen)

- Inference & Learning:
- We have Y & Xdata in our model
- But we don’t know the values of hidden variables: , M and their initial values
- We also don’t know the correct value of parameters: , M ,A,G and their initial values
- We solve these problems in Bayesian paradigm, using EM Algorithm.

Steve Djajasaputra (SNN Nijmegen)

Steps:

- Training step: find the model parametersand hidden variables 1:T given the data from observation window X1:T,Y1:T, using EM algorithm and Kalman smoothing.
- Forecasting step: predict T+h and YT+hh is the horizon of forecasting
- Updating step: update the hidden variables 1:T+h given the real value YT+h
- Repeat the forecasting & updating steps above in iterations.

Steve Djajasaputra (SNN Nijmegen)

- 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.

Steve Djajasaputra (SNN Nijmegen)

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

Steve Djajasaputra (SNN Nijmegen)

- 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.

Steve Djajasaputra (SNN Nijmegen)

- To validate our model.
- It’s 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

Steve Djajasaputra (SNN Nijmegen)

- 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

Steve Djajasaputra (SNN Nijmegen)

- 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

Steve Djajasaputra (SNN Nijmegen)

- 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

Steve Djajasaputra (SNN Nijmegen)

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

Steve Djajasaputra (SNN Nijmegen)

- However, we don’t 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.

Steve Djajasaputra (SNN Nijmegen)

Steve Djajasaputra (SNN Nijmegen)

- 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.

Steve Djajasaputra (SNN Nijmegen)

- 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.

Steve Djajasaputra (SNN Nijmegen)

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

Steve Djajasaputra (SNN Nijmegen)

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

Steve Djajasaputra (SNN Nijmegen)

- On Observed data Y

Steve Djajasaputra (SNN Nijmegen)

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

Steve Djajasaputra (SNN Nijmegen)