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A GARCH model is employed to help predict volatility (i.e. of stocks, XE rates etc) based on historical values through model fitting. Recent data is given more significance than older data.

Compare to the least squares approach, which weights all the data equally. Since volatility is not the same across the entire data set (periods of volatility cluster together), this assumption is not valid.

The related link provides greater detail and an Excel spreadsheet

Q: What is a GARCH model?

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GARCH processes are used to model the conditional volatility of financial returns in discrete time. There are many many different types of GARCH, the most popular and simplest being the GARCH(1,1), where returns have mean mu and conditional variance vt (t indexes time): returnt = mu + sqrt(vt)et where et is a standardized innovation.Conditional variance follows a first order autoregressive process: vt= a + b* vt-1 + c* vt-1*et-1^2

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GARCH processes are used to model the conditional volatility of financial returns in discrete time. There are many many different types of GARCH, the most popular and simplest being the GARCH(1,1), where returns have mean mu and conditional variance vt (t indexes time): returnt = mu + sqrt(vt)et where et is a standardized innovation.Conditional variance follows a first order autoregressive process: vt= a + b* vt-1 + c* vt-1*et-1^2

Luc Bauwens has written: 'Handbook of volatility models and their applications' -- subject(s): BUSINESS & ECONOMICS / Finance, Econometric models, GARCH model, Banks and banking, Finance 'Bayesian inference in dynamic econometric models' -- subject(s): Bayesian statistical decision theory, Econometric models 'Handbook of volatility models and their applications' -- subject(s): BUSINESS & ECONOMICS / Finance, Econometric models, GARCH model, Banks and banking, Finance

You need to set up an objective function via Maximum Likelihood Estimation, and then use Excel's Solver to maximize it for estimation parameters. Check out the attached link for an example Excel spreadsheet

Because they are intuitive, very tractable and easy to estimate. Furthermore, they capture reasonably well the most important stylized facts of volatility, such as 'volatility clustering' (the tendency of large observations to be followed by other large observations and of small observations to be followed by other small observations) and leptokurtosis (fat tails).

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