Conditional volatility models

The time-varying nature of the variance may be captured using conditional time
series models. Unlike historical volatility models, this class of statistical models make
more effective use of the information set available at time t to estimate the means and variances as varying with time. One type of model that has been successful in
capturing time-varying variances and covariances is a state space technique such as
the Kalman filter. This is a form of time-varying parameter model which bases
regression estimates on historical data up to and including the current time period.
A useful attribute of this model lies in its ability to describe historical data that is
generated from state variables. Hence the usefulness of Kalman filter in constructing
volatility forecasts on the basis of historical data. Another type of model is the
conditional heteroskedastic models such as the Autoregressive Conditional Heteroskedastic
(ARCH) and the generalized ARCH (GARCH). These are designed to remove
the systematically changing variance from the data which accounts for much of the
leptokurtosis in the distribution of speculative price changes. Essentially, these
models allow the distribution of the data to exhibit leptokurtosis and hence are better
able to describe the empirical distribution of financial data.