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I have a dataset consisting of many product sales over time on a daily basis. I do know when promotions and discounts happen with four months in advance.

When there are no promotions sales are 0 or very very low. However, when there is a promotion or (several promotions for a single product) sales really increase, so it makes the series to explode for the promotion period.

I am trying to forecast sales for each product the following month.

The problem I am facing is that I have tried to model the data as a time series, however I believe there is not a clear time series structure, because:

1.- I know when promotions are going to occurr and then when sales are going to peak.

2.- Time series tries to forecast demand based on past values, however we know when and why this happened, so there is not a "hidden" pattern/structure. Time itself doesn't seem to influence.

I have read about intermittent time series, hurdle model.. but I am not sure if this is the right way to proceed. Maybe instead of using a time series model a causal model may perform better e.g. linear regression, Zero Inflated Negative Binomial, ZIP... Someone has suggested me to use a Quantile regression but not sure if this may work.

I have applied linear and poisson models and seem to have quite a good fitness.

Any suggestion on what is the best way to proceed with such a problem: time series or causal modelling?

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    $\begingroup$ why not a mixed effects model? This would allow you to account for both regular time-series patterns as well as promotions. $\endgroup$ – Ujjwal Kumar Jan 17 '17 at 13:04
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Time series data can be low (with some negative side-effects) but problems arise with consecutive values that are alike .e.g. 1,1,1,1,1,1,0,0,0,0,0,0,0,0,0 . Data like this can inject false auto-correlation. It is possible to combine both regression structure reflecting known causals and memory (ARIMA) structure reflecting unknown/unspecified stochastic causals while conditioning for unknown/unspecified deterministic structure such as level/step shifts and others.

This is known as a Transfer Function or a Dynamic Regression as there may be lead and lag effects around your promotions. When I know that something is going to be cheaper tomorrow, I normally defer my purchase. I suggest you review some of my posts and other posts on these topics. If you wish I might be able to demonstrate the art of the possible if you post your data in a column oriented excel file or a csv file.

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