# Croston forecasting initialization

I have been working with the Croston method but I have many doubts and I do not know if you can help me!
The method says that if demand $$x_t$$ at period $$t$$ is $$x_t= 0$$ then $$\hat{z}(t) = \hat{z}(t-1)$$ and $$\hat{n}(t) = \hat{n}(t-1)$$, but what do we do at the first observation? How do we initialize the variables $$z(t)$$ and $$n(t)$$, if it is the first period we do not have the previous value?

Another question ... I have a historical period of 20 months and with very low demand values (ex: 0,1,0,0,0,0,0,0,0,0,0,1,1,0,8,0,0,0,0,0), do you think it is correct to use the croston method? Or is there a better method for this type of search with these values?
I do not know if my question is stupid, I have researched a lot but I don't find much information, I hope you can help me!

• I do not see what is "unclear what you're asking" about this question. I see two straightforward questions about crostons-method, which to me appear clear enough to answer. Please reopen. – Stephan Kolassa Jun 12 '19 at 15:29

## 1 Answer

1. Initialize the smoothed series in some "reasonable" manner. For instance, initialize $$\hat{z}_1$$ as the average nonzero transaction, and $$\hat{n}_1$$ as the average period between transactions.

Don't overthink this. Croston's method is ad hoc, anyway. See, e.g., Shenstone & Hyndman (2005) on the non-existence of a statistical model underlying it, and Syntetos & Boylan (2005) on the bias of the point prediction and a debiasing term.

2. As to whether it is "correct" to use Croston's method: first of all, note that there is no coherent statistical justification for Croston, so a pure statistician would answer that it's never "correct".

As a forecaster (which is a different animal than a statistician), I would reply that I see very few reasonable uses for an expectation point forecast for intermittent demand. If you have a demand of size 1 every 10 periods, or a lumpy demand of 10 every 100 periods, then an unbiased expectation forecast will be 0.1 in both cases... but the amount of stock you need to carry will differ radically between the two cases.

So whether Croston's (or any other method) is "correct" will depend on what you plan on using the forecast for. Croston won't give you prediction intervals for safety amounts, for instance.

• "Croston won't give you prediction intervals for safety amounts, for instance." - the Oracle software that we use does provide prediction intervals for Croston's, and I can't get a straight forward answer from Oracle on how they are calculating it (Proprietary information blah, blah, !#$~!#$~@#$!@#,...) – Skander H. - Reinstate Monica Jun 11 '19 at 18:20 • @SkanderH.: you can, of course, use the Croston expectation forecast as the parameter for a Poisson distribution. Or estimate the overdispersion and use a negbin. – Stephan Kolassa Jun 11 '19 at 18:29 • No that's not how they're doing it. In the Oracle retail suite, using Poisson for slow movers is handled by a separate replenishment package which consumes raw forecasts from the forecast engine. The actual forecasting tool outputs both a forecast and an interval even when the method setting is Croston's. – Skander H. - Reinstate Monica Jun 11 '19 at 18:49 • @SkanderH.: interesting. And a bit strange. I'd recommend you look at other retail forecasting engines (ahem), but we have a lot of Proprietary information blah, blah, !#~!#~@#$!@#, which I'm not allowed to talk about, too... – Stephan Kolassa Jun 11 '19 at 18:57
• The whole proprietary information concept is make it difficult for teams like my own (mostly an engineering team tasked with implementing existing forecasting packages) in the face of in house data science leaders claiming that if we are not building our own custom models, we should at least know the math involved in the models we are deploying from the vendor. Oracle at least has the basic forecasting methods explained (and details about how the reconciliation is made across the hierarchy, and how model selection works) but still doesn't give us all the details. – Skander H. - Reinstate Monica Jun 11 '19 at 19:07