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fter reading this chapter you will understand:■ (^) The concepts of homoscedasticity and heteroscedasticity.
■ (^) The concept of conditional heteroscedasticity.
■ (^) The empirical basis for conditional heteroscedasticity.
■ (^) Autoregressive modeling of conditional heteroscedasticity.
■ (^) Autoregressive conditional heteroscedasticity (ARCH) models.
■ (^) Extensions of ARCH models: generalized autoregressive conditional
heteroscedasticity (GARCH) models and multivariate ARCH models.
■ (^) How to apply estimation software for ARCH models.
In Chapter 9, we described a time series tool, the autoregressive mov-
ing average (ARMA) model, that focuses on estimating and forecasting the
mean. Now we turn to financial econometric tools that are used to estimate
and forecast an important measure in finance: the variance of a financial
time series. The variance is an important measure used in the quantification
of risk for a portfolio or a trading position, strategies for controlling the risk
of a portfolio or a trading position (i.e., determination of the hedge ratio),
and as an input in an option pricing model.
Among the financial econometric tools used for forecasting the con-
ditional variance, the most widely used are the autoregressive conditional
heteroscedasticity (ARCH) model and the generalized autoregressive condi-
tional heteroscedasticity (GARCH) model.^1 These tools are described in this
chapter along with a brief description of variants of these models. Estima-
tion of the forecasted correlation between major asset classes or any two
financial assets in the same asset class is calculated based on the forecasted
(^1) Other tools include stochastic volatility models and Markov switching models.
chApter
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