Conditional or unconditional volatility?

Question

I am reading a paper (reference below) that states "The conditional volatility for each underlying security (or for a market index) can be estimated using the standard deviation of the stock’s periodic returns. However, since volatilities are persistent, as we have learned from the ARCH literature, such an estimator of volatility will be biased and inefficient, as shown by Chou (1988)....."

Why is this a "conditional" volatility? To me it seems like you can't possibly get any more unconditional than taking a simple standard deviation over past returns.

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"Investigating the Behavior of Idiosyncratic Volatility" by Xu and Malkiel in the Journal of Business (2003).

Answer 1

In terms of ARCH conditional variance is the variance conditional on past information (i.e. the history of the process). This is useful for modeling a process that exhibits volatility clustering. Perhaps he means that starting with the standard deviation (unconditional volatility) of stock returns one can then use that as an input to estimate the conditional volatility.

Edit: Some notes on ARCH models and conditional volatility