croston's model

[qkaiwei]

When looking though the illustration of croston's model in SAS help, the help explians the initialization of the model, that's when the starting time t=1:

the level of q(1)=max[q(1), the level of q(0)], where the level of q(0) is  is the final backcast level state.

So please tell me what's  the final backcast level state, if possible.

Thanks!

[udo_sas]

Hello -

As you know Croston's method is based on the following assumption: an intermittent time series (demand series) can be decomposed into two components: a demand interval series and a demand size series. Croston’s method models and forecasts each component independently, then combines the two forecasts. By treating each component of the demand series as a time series based on the demand index, optimal smoothing parameters can be estimated and predictions for each component can be computed using nonseasonal exponential smoothing methods (simple, double, linear, and damped-trend) as well as their transformed versions.

The section of our documentation you are referring to deals with the question of how to adress the the smoothing state initialization of Exponential Smoothing Models challenge.

You will find a detailed description of the process here: http://support.sas.com/documentation/cdl/en/hpfug/63959/HTML/default/viewer.htm#hpfug_hpfdet_sect005...

In particular you might be interested in: http://support.sas.com/documentation/cdl/en/hpfug/63959/HTML/default/viewer.htm#hpfug_hpfdet_sect008...

As you will find the "final backcast level state" is an appropriate choice for the initial smoothing state is made by backcasting from time t=n to t=1 to obtain a prediction at t=0.

Thanks,
Udo