Error of VAR by overlapping intervals

When overlapping intervals in time series are used, volatility and price changes' percentiles are underestimated. Consequently, value-at-risk is also underestimated. Heng Sun, Izzy Nelken, Guowen Han and Jiping Guo measure the size of this underestimation

There are many applications in which the long-term statistical properties of short-term financial time series are required. For example, we might be interested in obtaining the 1% worst monthly return. That is, out of 200 months, we need the second-worst monthly performance. Requirements for such statistics arise, for example, when we look at value-at-risk estimates using the historical simulation method. In this method, it is common to look at the actual historical movements in the risk factors