What Volatility GARCH Estimates and Forecasts

Summary

The answers clarify that a standard GARCH model is fitted to a time series of returns to estimate conditional variance, with its parameters determining how past shocks and prior variance inform the current estimate. Taking the square root of conditional variance gives volatility in standard deviation terms. This estimate is based on historical return observations and their chosen weighting through the model; it is not implied volatility extracted from option prices.

Once calibrated, GARCH is commonly used to forecast volatility over future horizons. Its forecasts describe conditional future return volatility under the model, rather than guaranteeing the volatility that will actually occur. The answer also points out that different GARCH variants may be suitable for different time series, and mentions persistence as a feature related to how slowly variance returns toward its long-run level. The discussion is introductory and does not specify a model variant, estimation method, forecast horizon, or validation procedure.

Key ideas

• GARCH models estimate conditional variance from a historical return series.
• The square root of conditional variance expresses the estimate as volatility or standard deviation.
• After calibration, GARCH can generate forecasts of future conditional return volatility.
• Forecasts depend on model specification and do not equal realized future volatility.

Tags

# what volatility do we calculate using GARCH model


# what volatility do we calculate using GARCH model












what volatility do we calculate using GARCH model, Historical vol or Implied vol or Future Vol or Actual vol.

## Answer by SolitonK (score 2)

https://quant.stackexchange.com/a/15584

In the case of application in finance, usually, GARCH is used in estimating realized volatility of returns based on the weight we would like to give to each past observation.

Ultimately after estimating (calibrating) the parameters of the model to an existing time-series, GARCH is used for forecasting multi-step ahead return (future) volatility.

Different variants of the GARCH model exist and the application of each one depends on the properties of the time-series to be examined. Some of them can be found Here.

## Answer by Rime (score 0)

https://quant.stackexchange.com/a/15583

From my understanding I believe you will calculate conditional variance with GARCH. You would then need to take the square root of the variance to calculate the standard deviation/ volatility. One key aspect in GARCH is that you can calculate the "persistence" , I.e. How likely is the asset to "persist" to its long run variance

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.