The basic historical simulation approach assumes that each day in the past is given equal weight. More formally, if we have observations for n day-to-day changes, each of them is given a weighting of 1/n. However, it is possible to adjust the basic historical simulation approach for nonstationarity in market variables, and allocate more weights to more recent observations.
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Basic historical simulation gives equal weights to all the observations in the past. This is a shortcoming as the fact that predictions depend more on the recent observations than in the past.
The basic historical simulation can be tweaked by giving more weights to more recent observations and lower weights as the observations time goes away from the curren time. This is called as Weighted Historical simulation. Different kinds of weights such as exponential can be allocated here.
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