A simple measure of asset return
volatility is its variance over time. If we have data for stock returns over,
say, a period of 1,000 days, we can compute the variance of daily stock returns
by subtracting the mean value of stock returns from their individual values,
square the difference and divide it by the number of observations. By itself it
does not capture volatility clustering because it is a measure of what is
called unconditional variance, which is a single number for a given sample. It
does not take into account the past history of returns. That is, it does not
take into account time-varying volatility in asset returns. A measure that
takes into account the past history is known as autoregressive conditional
heteroscedasticity, or ARCH for short.[1]
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