Processes with Autoregressive Conditional Heteroskedasticity (ARCH)

Abstract

In particular in the case of financial time series one often observes a highly fluctuating volatility (or variance) of a series: Agitated periods with extreme amplitudes alternate with rather quiet periods being characterized by moderate observations. After some short preliminary considerations concerning models with time-dependent heteroskedasticity, we will discuss the model of autoregressive conditional heteroskedasticity (ARCH), for which Robert F. Engle was awarded the Nobel prize in the year 2003. After a generalization (GARCH), there will be a discussion on extensions relevant for practice.