Historical simulation in finance's value at risk (VaR) analysis is a procedure for predicting value at risk by 'simulating' or constructing the cumulative distribution function (CDF) of assets returns over time. Unlike most parametric VaR models, Historical Simulation does not assume any distribution on the asset returns. Also, it is relatively easy to implement. However, there is a couple of shortcomings of historical simulation, and first of all is that it imposes a restriction on the estimation assuming asset returns are independent and identically-distributed (iid) which is not the case. From empirical evidence, it is known that asset returns are clearly not independent as they exhibit certain patterns such as volatility clustering. Therefore it can be unrealistic to assume iid asset returns. Second restriction relates to time. Historical simulation, it applies equal weight to all returns of the whole period and this is inconsistent with the nature where there is diminishing predictability of data that are further away from the present. These two shortcomings leads economists and financial experts to further develop other non-parametric, semi-parametric and parametric models.
Like the traditional historical simulation technique, 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 iid asset returns. [1]
Filtered historical simulation is a semi-parametric technique in forecasting VaR. The returns in this case are no longer assumed to be iid, rather there is an additional innovation term v is now assumed to be iid instead. This allows the means and variances to be 'filtered away', coupled with an empirically estimated CDF, it becomes a more realistic model in predicting VaR.[2]
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