Transcription of 18 GARCH Models - University of Washington
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18 GARCH Models - University of Washington
18 GARCH IntroductionAs seen in earlier chapters, financial markets data often exhibit volatilityclustering, where time series show periods of high volatility and periods of lowvolatility; see, for example, Figure In fact, with economic and financialdata, time-varying volatility is more common than constant volatility, andaccurate modeling of time-varying volatility is of great importance in we saw in Chapter 9, ARMA Models are used to model the conditionalexpectation of a process given the past, but in an ARMA model the con-ditional variance given the past is constant. What does this mean for, say,modeling stock returns? Suppose we have noticed that recent daily returnshave been unusually volatile. We might expect that tomorrow s return is alsomore variable than usual. However, an ARMA model cannot capture thistype of behavior because its conditional variance is constant. So we need bet-ter time series Models if we want to model the nonconstant volatility.
ARCH is an acronym meaning AutoRegressive Conditional Heteroscedas-ticity. In ARCH models the conditional variance has a structure very similar to the structure of the conditional expectation in an AR model. We flrst study the ARCH(1) model, which is the simplest GARCH model and similar to an AR(1) model.
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