R data.table difference equation (dynamic panel data) - r

Question

I have a data table with a column v2 with 'initial values' and a column v1 with a growth rate. I would like to extrapolate v2 for years past the available value, by growing the previous value by factor v1. In 'time series' notation v2(t+1)=v2(t)*v1(t), given a v2(0).
The problem is, the year of the initial value may vary by group x in the dataset. In some groups, v2 may be available in multiple years, or not at all. Also, the number of years per group may vary (unbalanced panel). Using the shift function does not help, because it shifts v2 once, and does not reference the previously update value.
x year v1 v2
1: a 2012 0.8501072 NA
2: a 2013 1.0926093 39.36505
3: a 2014 1.2084379 NA
4: a 2015 0.8921997 NA
5: a 2016 0.8023251 NA
6: b 2012 1.1005287 NA
7: b 2013 1.0139800 NA
8: b 2014 1.1539676 NA
9: b 2015 1.2282501 NA
10: b 2016 0.8052265 NA
11: c 2012 0.8866425 NA
12: c 2013 0.9952566 44.30377
13: c 2014 0.9092020 NA
14: c 2015 1.0295864 15.04948
15: c 2016 0.8812966 NA
The value of V2, x=a, year=2014 should be 39.36*1.208, and in 2015 that answer times 0.89.
The following code, in a set of loops, works and does what I want:
ivec<-unique(DT[,x])
for (i in 1:length(ivec)) {
tvec<-unique(DT[x==ivec[i] ,y])
for (t in 2:length(tvec)) {
if (is.na(DT[x==ivec[i] & y==tvec[t], v2])) {
DT[x==ivec[i] & y==tvec[t],v2:=DT[x==ivec[i] & y==tvec[(t-1)],v2]*v1]
}
}
}

Answer 1

Try this:
DT[, v2:= Reduce(`*`, v1[-1], init=v2[1], acc=TRUE), by=.(x, cumsum(!is.na(v2)))]
# x year v1 v2
# 1: a 2012 0.8501072 NA
# 2: a 2013 1.0926093 39.36505
# 3: a 2014 1.2084379 47.57022
# 4: a 2015 0.8921997 42.44213
# 5: a 2016 0.8023251 34.05239
# 6: b 2012 1.1005287 NA
# 7: b 2013 1.0139800 NA
# 8: b 2014 1.1539676 NA
# 9: b 2015 1.2282501 NA
# 10: b 2016 0.8052265 NA
# 11: c 2012 0.8866425 NA
# 12: c 2013 0.9952566 44.30377
# 13: c 2014 0.9092020 40.28108
# 14: c 2015 1.0295864 15.04948
# 15: c 2016 0.8812966 13.26306