# 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. 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.
• "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