Croston forecasting initialization I have been working with the Croston method but I have many doubts.
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 (e.g. 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?  
 A: *

*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.

*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.
