ON THE RELATION BETWEEN GARCH AND STABLE PROCESSES

Stable and GARCH processes have been advocated for modeling financial data. The aim of this note is to compare the two processes. It is shown that the unconditional distribution of variates from a GARCH-like process, which explicitly models the clustering of volatility and exhibits the fat-tail property as well, can be stable. Given suitable conditions the conditional distributions are stable as well. While it is generally realized that processes with variates that have unconditional nonnormal stable densities have a high frequency of 'outliers', it is less well known that they can exhibit the clustering phenomenon too. The clustering is obtained through stable subordination with conditional scaling.