# Rolling Winsorization for Time-Series

I'm running a multivariate time series analysis and need to deal with some outliers. I'm thinking about using a rolling winsorization (e.g., pull anything above 99.5 percentile and replace with the 99.5 percentile value). The look back period would start at 2-years and continue to expand as I moved forward in the time series. Is this an appropriate way to deal with outliers? I have a few six sigma moves in a dataset of >3,000.

## 1 Answer

### Winsorization is fine, but carefully analyze your data and think about the nature of your outliers!

I assume you are aware of this answer here:

[...] So you have to be extremely careful and double check all the data points you remove by whatever available method out there! [...]

Financial data are notoriously subject to outliers. In many statistical analyses, such data points may exert an undue influence on the results, making the results unreliable. Commonly, empirical asset pricing researchers usually take an ad hoc approach to dealing with outliers (instead of several statistical methods that are designed to assess the effect of outliers).

Winsorization is performed by setting the values of a variable $$X_n$$ with $$n$$ observations, that are in the top $$h$$ percent of all values of $$X$$, to the $$(100-h)$$th percentile of $$X$$. Similarly, values of $$X$$ in the bottom $$l$$ percent of $$X$$ values are set to the $$l$$-th percentile of $$X$$.

Truncation is very similar to winsorization, except instead of setting the values of $$X$$ above $$Pctl_h(X)$$ to $$Pctl_h(X)$$, we set them to missing or unavailable. Similarly, values of $$X$$ that are less than $$Pctl_l(X)$$ are taken to be missing.

Bali/Engle/Murray (2016) state (p. 6):

When to use winsorization or truncation is a difficult question to answer because some outliers are legitimate while others are data errors. In a statistical sense, one might argue that truncation should be used when the data points to be truncated are believed to be generated by a different distribution than the data points that are not to be truncated. Winsorization is perhaps preferable when the extreme data points are believed to indicate that the true values of the given variable for the entities whose values are to be winsorized are very high or very low, but perhaps not quite as extreme as is indicated by the calculated values. Most empirical asset pricing researchers choose to use winsorization instead of truncation. However, if the results of an analysis are substantially impacted by this choice, they should be viewed with skepticism.