I am now working on a set of time series data and I would like to quantify the series' volatility.
I have think of an approach which is first model it as some auto-regressive model like ARCH and compute the sum of squared residuals between the model and the real data.
Does it make any sense?
After you have accounted for the ARIMA structure AND any Pulses/Level Shifts/Seasonal Pulses/Local Time Trends AND any changes in parameters over time, one can test for non-constant variance via http://www.unc.edu/~jbhill/tsay.pdf . The volatility can be measured by computing the mean-square error of the final models residuals. If constant variance can't be rejected then one could square the errors and compute the ACF which can be used to characterize the volatility of the error series and thus the volatility of the original series.
