clean.boudt(R, alpha = 0.01, trim = 0.001)
There are two main approaches in defining robust alternatives to estimate the multivariate moments by their sample means (see e.g. Maronna[2006]). One approach is to consider a more robust estimator than the sample means. Another one is to first clean (in a robust way) the data and then take the sample means and moments of the cleaned data.
Our cleaning method follows the second approach. It is designed in such a way that, if we want to estimate downside risk with loss probability $alpha$, it will never clean observations that belong to the $(1-alpha)$ least extreme observations. Suppose we have an $n$-dimensional vector time series of length $T$: $r_1,...,r_T$. We clean this time series in three steps.
Note that the primary value of data cleaning lies in creating a more robust and stable estimation of the distribution describing the large majority of the return data. The increased robustness and stability of the estimated moments utilizing cleaned data should be used for portfolio construction. If a portfolio manager wishes to have a more conservative risk estimate, cleaning may not be indicated for risk monitoring. It is also important to note that the robust method proposed here does not remove data from the series, but only decreases the magnitude of the extreme events. It may also be appropriate in practice to use a cleaning threshold somewhat outside the VaR threshold that the manager wishes to consider. In actual practice, it is probably best to back-test the results of both cleaned and uncleaned series to see what works best with the particular combination of assets under consideration.
Khan, J. A., S. Van Aelst, and R. H. Zamar (2007). Robust linear model selection based on least angle regression. Journal of the American Statistical Association 102.
Maronna, R. A., D. R. Martin, and V. J. Yohai (2006). Robust Statistics: Theory and Methods. Wiley.
Rousseeuw, P. J. (1985). Multivariate estimation with high breakdown point. In W. Grossmann, G. Pflug, I. Vincze, and W. Wertz (Eds.), Mathematical Statistics and Its Applications, Volume B, pp. 283?297. Dordrecht-Reidel.
Return.clean