Using order book data to enhance your statistical forecast

The vast majority of companies rely on statistical forecast models to predict their demand. These models use time series of historical sales to estimate future demand. A key assumption of these models is that the underlying system remains unchanged. In other words; the relationship between historical and future demand does not change. Clearly this assumption is violated during the current Corona crisis and as a result we should be very reluctant to rely on statistical models. The current circumstances present both a need and an opportunity to predict demand more dynamically. This requires different information than just historical sales; it requires tapping into other data sources that provide insights regarding future demand. One of these data sources to consider are the open orders from your order book.

What exactly are open orders?

Open orders refer to demand that has been placed in advance. In other words, it constitutes future demand that is already known at present. Although many companies have access to open orders via their order book, this information rarely finds its way into the statistical forecast. At best, planners use this information manually to adjust the statistical forecast. It would be more efficient, however, if the statistical forecast could somehow already take this information into account. Sure, that sounds good, but how can we do this? Well, 18th century clergyman and mathematician Thomas Bayes provides us with an interesting toolkit to take on this problem.

Bayesian inference

Before we jump right into it, let’s take a moment to discuss the basics of Bayesian inference. Bayes’ Theorem provides us with a quantitative framework for updating our beliefs as the facts around us change or new information arises. This framework is captured in his famous equation:

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Although the formula might look intimidating at first, what it essentially boils down to is this: whenever we receive new information, how much should we let it affect what we currently believe to be true? Does the new information support the initial belief, dispute it, or not affect it all? Are you starting to see how this method might help in incorporating order book data into the statistical forecast?

Applying the Bayesian line of reasoning to our forecast problem

The statistical forecast provides us with the initial belief regarding what the demand will be in the future. By contemplating the order book, however, we receive new information that will either support or dispute this initial belief. Using Bayes’ equation, we can then calculate the Posterior distribution. This distribution represents our belief regarding future demand after taking into account both the initial statistical forecast and the open orders. 

Example

Let’s clarify with an example. Imagine that your (initial) statistical forecast for one month ahead is 24. Moreover, your order book shows that, at present, you have 6 pre-orders in the system for one month ahead. Finally, the last piece of information that we need is an estimate of the probability that an order for next month is already known at present. Assume that this probability is equal to 50%. The question now becomes ‘How to use the number of pre-orders to adjust the initial statistical forecast?’. 

  1. The first step is to fit a distribution with mean equal to the initial forecast (in our example 24). This distribution (in blue) represents our initial belief about what the demand for next month is going to be.
  2. Next, we use Bayes’ rule to adjust the initial forecast. To put it plainly, in this example the order book tells us that future demand is likely to be lower than we initially expected based on the statistical forecast. Hence, the Bayesian forecast incorporates this information and lowers the statistical forecast (from 24 to 19). 
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Final thoughts 

As a consequence of the Corona crisis, it is possible that your market is currently facing drops in demand, increases in demand, or significant demand shifts over time or between products. In any case, your order book might provide valuable information, signalling where your future demand is heading. With the Bayesian toolkit, you can incorporate this information automatically without having to check every order yourself.

Eager to learn more about this topic or curious if this method could also be valuable for your organisation? Please do reach out to Rijk van der Meulen.