[1] Unlike parametric VaR models, historical simulation does not assume a particular distribution of the asset returns.
Traditional historical simulation applies equal weight to all returns of the whole period; this is inconsistent with the diminishing predictability of data that are further away from the present.
Weighted historical simulation applies decreasing weights to returns that are further away from the present, which overcomes the inconsistency of historical simulation with diminishing predictability of data that are further away from the present.
However, weighted historical simulation still assumes independent and identically distributed random variables (IID) asset returns.
[3] Filtered historical simulation tries to capture volatility which is one of the causes for violation of IID.