Let us assume that each month of the year (up to November) we calculate a VaR (say 99%) with holding period to the end of the year. Thus the holding period starts with 12 months and goes down to 1 month in November.
Obviously the event of a breach of my June VaR is not independent of the event of a breach of my Augus VaR (similar to here).
So how can I calculate the significance of the number of breaches? How can I take the dependence into account?
PS: At first sight it looks a bit artificial but a lot of institutions want to measure their risk in an (accounting) year. The next step is VaR and its backtest.
If look at monthly log-returns then in October I estimate $$ P[R_1+ R_2 + R_3 \le VaR_1] $$ and in November I look at $$ P[R_2 + R_3 \le VaR_2]. $$
Another edit: Say I estimated my VaR in Jan, Feb, up to Novenber and in December the market drops by 50%. Then I can have a breach in all my VaR estimates.
In the usual setting I estimate VaR and check on the following period. Then I estimate VaR again and check on the next period. Thus there is no overlap and the above problem can not happen!
I could only form series of "estimate yearly loss in Month x" and e.g. look at all January VaRs for the year 2000, 2001, .. 2016. They would be (more or less) independent. Then I could look at Februaries ... this would take away the overlap. But I would only have a few observations.