## Documentation Center |

Consider the time series

where
. Here, *z _{t}* is
an independent and identically distributed series of standardized
random variables. Econometrics Toolbox™ supports standardized Gaussian
and standardized Student's

A *conditional variance model* specifies
the dynamic evolution of the innovation variance,

where *H*_{t–1} is
the history of the process. The history includes:

Past variances,

Past innovations,

Conditional variance models are appropriate for time series that do not exhibit significant autocorrelation, but are serially dependent. The innovation series is uncorrelated, because:

*E*(*ε*) = 0._{t}*E*(*ε*_{t}*ε*) = 0 for all_{t–h}*t*and

However, if
depends on
, for example, then *ε _{t}* depends
on

Two characteristics of financial time series that conditional variance models address are:

*Volatility clustering*. Volatility is the conditional standard deviation of a time series. Autocorrelation in the conditional variance process results in volatility clustering. The GARCH model and its variants model autoregression in the variance series.*Leverage effects*. The volatility of some time series responds more to large decreases than to large increases. This asymmetric clustering behavior is known as the leverage effect. The EGARCH and GJR models have leverage terms to model this asymmetry.

- Specify GARCH Models Using garch
- Specify EGARCH Models Using egarch
- Specify GJR Models Using gjr
- Specify Conditional Mean and Variance Models

Was this topic helpful?