# In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) volatility measurement if one is not interested in forecasting future volatility?

For context, as mentioned in a comment below, I need a measure of past monthly volatility to study the relationship between (monthly) mutual fund alphas and (monthly) market volatility over a past period of time.

• Do you want some time specific measure of volatility $\sigma^2_t$? The simplest possible thing to do is estimate based upon some rolling window. Volatility models such as GARCH can also be used to back out some estimated $\sigma^2_t$ process from the data. – Matthew Gunn May 18 '19 at 17:24
• What would be the benefits of using a GARCH model instead of a simple moving average standard deviation in the context of in-sample estimation, if any? – Gianluca May 18 '19 at 20:28
• When you compute std deviation for a subperiod $[T_1,T_2]$ you get a single number $\sigma_{T_1,T_2}$ which you can think of as an average over all days in $T_1,T_2$ of something called the "latent volatility" or "instantaneous volatility" on each day. This instantaneous volatility is not observable but you might estimate it with a model such as GARCH. This is a possible benefit of a model. But my question for you is: what do you need volatility for? – noob2 May 18 '19 at 21:26
• I need a measure of past monthly volatility to study the relationship between (monthly) mutual fund alphas and (monthly) market volatility over a past period of time. Based on what you say, it seems to me that using GARCH would only make sense if I wanted to estimate daily volatilities. I am trying to understand whether measures other than the monthly standard deviation could be of any use when measuring monthly volatility. Would estimating daily volatilities with GARCH and then converting them into monthly volatilities have any benefit in this context? – Gianluca May 19 '19 at 12:50
• I believe you do not need GARCH for your application – noob2 May 20 '19 at 19:56