Moving average with dynamic window - r

Question

I'm trying to add a new column to my data table that contains the average of some of the following rows. How many rows to be selected for the average however depends on the time stamp of the rows.
Here is some test data:
DT<-data.table(Weekstart=c(1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,9),Art=c("a","b","a","b","a","a","a","b","b","a","b","a","b","a","b","a"),Demand=c(1:16))
I want to add a column with the mean of all demands, which occured in the weeks ("Weekstart") up to three weeks before the respective week (grouped by Art, excluding the actual week).
With rollapply from zoo-library, it works like this:
setorder(DT,-Weekstart)
DT[,RollMean:=rollapply(Demand,width=list(1:3),partial=TRUE,FUN=mean,align="left",fill=NA),.(Art)]
The problem however is, some data is missing. In the example, the data for the Art b lack the week no 4, there is no Demand in week 4. As I want the average of the three prior weeks, not the three prior rows, the average is wrong. Instead, the result for Art b for week 6 should look like this:
DT[Art=="b"&Weekstart==6,RollMean:=6]
(6 instead of 14/3, because only Week 5 and Week 3 count: (8+4)/2)
Here is what I tired so far:
It would be possible to loop through the minima of the week of the following rows in order to create a vector that defines for each row, how wide the 'width' should be (the new column 'rollwidth'):
i<-3
DT[,rollwidth:=Weekstart-rollapply(Weekstart,width=list(1:3),partial=TRUE,FUN=min,align="left",fill=1),.(Art)]
while (max(DT[,Weekstart-rollapply(Weekstart,width=list(1:i),partial=TRUE,FUN=min,align="left",fill=NA),.(Art)][,V1],na.rm=TRUE)>3) {
i<-i-1
DT[rollwidth>3,rollwidth:=i]
}
But that seems very unprofessional (excuse my poor skills). And, unfortunately, the rollapply with width and rollwidth doesnt work as intended (produces warnings as 'rollwidth' is considered as all the rollwidths in the table):
DT[,RollMean2:=rollapply(Demand,width=list(1:rollwidth),partial=TRUE,FUN=mean,align="left",fill=NA),.(Art)]
What does work is
DT[,RollMean3:=rollapply(Demand,width=rollwidth,partial=TRUE,FUN=mean,align="left",fill=NA),.(Art)]
but then again, the average includes the actual week (not what I want).
Does anybody know how to apply a criterion (i.e. the difference in the weeks shall be <= 3) instead of a number of rows to the argument width?
Any suggestions are appreciated!