Comparing Sector Volatility with Historical Measures and GARCH
Summary
The document asks how to rank sectors by return volatility using daily prices and fitted GARCH models. It warns against comparing model orders or coefficients directly, since different series may require different specifications and parameter values do not provide an objective cross-sector volatility ranking.
For historical volatility, calculate return standard deviations over a chosen observation window and frequency, annualizing consistently to compare sectors. For forward-looking analysis, fit a GARCH-family model after accounting for linear time-series effects, then check residual dependence and distributional behavior. Use the resulting conditional volatility series to compare statistics such as minimum, maximum, and average, and examine forecasts and plots for clustering. The note distinguishes realized past variability from forecast volatility; rankings depend on the selected window, sampling frequency, model specification, and forecast horizon.
Key ideas
- Compare historical sector volatility using return standard deviations calculated over consistent windows and frequencies.
- Annualize volatility consistently when comparing return series at different sampling frequencies.
- For forecast volatility, fit an appropriate GARCH-family model and inspect residual diagnostics.
- Compare estimated volatility series and forecasts rather than ranking sectors by GARCH order or coefficients.
- Volatility rankings depend on the measurement period and whether the goal is retrospective or predictive.
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Full text
# How to user GARCH(p,q) to identify most volatile sector?
# How to user GARCH(p,q) to identify most volatile sector?
I would like to ask help concerning the utilization of GARCH(p,q) models to identify volatility. Suppose that I have daily closing prices of 6 financial sectors spanning several years, and I am interested in identifying which sector is the most and the least volatile (in terms of return). I have modeled their volatility using GARCH(p,q) and is now wondering how to use the estimated model to identify their volatility. Can I do the comparison by simply comparing the orders (perhaps, p) of their models? Or the coefficients?
P.S. I have a computation of historical volatility and am planning to supplement my findings with fitted GARCH(p,q) models. Can I do this?
## Answer by Robert Szóstakowski (score 1)
https://quant.stackexchange.com/a/20651
In the very begining I advice you to model always linear effects in the time series (ARMA models). Then you add a model which investigate ARCH effects (GARCH family). When you have done the models estimation part It is advised to check if residuals of the models do not show any dependiencies ( close to normal distribution, independent). In another step you calculculate the volatility of your time series using the calculated models and you can calculate their statistics ( min, max, average volatility). You can also calculate forecasts of the volatilities and compare them. It is worth checking the plots and analize how often do we have volatility clustering in our time series. Analizing the parameters of the model can be problematic becase you can get different models for different time series and how will you measure and compare them objectively.
## Answer by Richi Wa (score 0)
https://quant.stackexchange.com/a/20657
Volatility is a difficult object and it is not always clear what we mean when we use the word volatility.
I would make the following distinction as a first step:
- historical volatility: measuring the ex-post volatility of an asset/market/sector. You pick an observation period of interest (e.g. 3 months up to 3 years). You pick a frequency (often daily or weekly returns), calculate the standard deviation and annualize these numbers to make volatilities comparable (multiply by $\sqrt{250}$ if you use daily data, take $\sqrt{50}$ for weekly. Doing this you can find the time series that was most volatile in the past.
- ex-ante volatility: you want to predict/forecast volatility. Then do the above and chose an observation period together with a frequency and then fit a (G)ARCH model or something similar. Such models give you a forecast of each asset's volatility for the coming period in the future. Doing this you can estimate the time series that could be most volatile in the future.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.