GARCH in question ... and as a benchmark

GARCH models of volatility are ubiquitous. Over the past twelve years, the GARCH industry has produced an almost infinite number of volatility time series from an extremely wide range of return series. The main purpose of this paper is to revisit the notion of volatility. Although we stop just short of questioning the necessity (and certainly the success) of GARCH, we demonstrate that for at least one type of data - long term interest rates - it is possible to essentially reproduce GARCH volatility time series with simple moving averages of deviations from mean return. We also demonstrate (empirically) a functional relationship between GARCH(1,1) parameters and the optimal moving average window width. At the present time these results are based on the utilisation of GARCH volatility as a benchmark against which we select the optimal number of terms in the simple moving average representation. One possible avenue of research that might lead to the removal of this requirement is suggested. An interesting applied result that emerged from our analysis is this: from 1952 to the present, USA interest rate volatility has the highest overall cross-correlation with the interest rate volatilities of other countries. © 1999 Elsevier Science Inc. All rights reserved.