  The volatility of financial instruments is rarely constant, and usually
varies over time. This creates a phenomenon called volatility clustering, where
large price movements on one day are followed by similarly large movements on
successive days, creating temporal clusters. The GARCH model, which treats
volatility as a drift process, is commonly used to capture this behavior.
However research suggests that volatility is often better described by a
structural break model, where the volatility undergoes abrupt jumps in addition
to drift. Most efforts to integrate these jumps into the GARCH methodology have
resulted in models which are either very computationally demanding, or which
make problematic assumptions about the distribution of the instruments, often
assuming that they are Gaussian. We present a new approach which uses ideas
from nonparametric statistics to identify structural break points without
making such distributional assumptions, and then models drift separately within
each identified regime. Using our method, we investigate the volatility of
several major stock indexes, and find that our approach can potentially give an
improved fit compared to more commonly used techniques.
