Often, eliminating serial correlation refers to the process of taking a delta, described in this lecture: https://www.quantopian.com/lectures#Integration,-Cointegration,-and-Stationarity
Is that what is done in the JPM paper? I'm not actually clear on how you would 'eliminate' auto-correlation, do they then measure CVaR on the new series and try to transform that number back into returns space?
If the returns do not trend, most statistical methods for risk evaluation will be more reliable. However it is still possible to misrepresent the risk as future conditions may change. It's always an estimate, never a certain answer, and a very stable period may be followed by a regime change or period of high volatility.
De-meaning usually is used for normalization to bring all series into the same space. It shouldn't affect any trend in the data as subtracting a mean will preserve the trend.
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