An Empirical Analysis of Alternative Parametric ARCH Models

GEOFFREY F. LOUDON," WING H. WATT^ AND PRADEEP K. YADAVc*
"Macquarie University, Australia
b~~~ Bank, Singapore
'Department of Accounting and Finance, University of Strathclyde, 100 Cathedral Street, Glasgolr G4 OLN, UK
SUMMARY
This paper presents empirical evidence on the effectiveness of eight different parametric ARCH models in
describing daily stock returns. Twenty-seven years of UK daily data on a broad-based value weighted stock
index are investigated for the period 1971-97. Several interesting results are documented. Overall, the results
strongly demonstrate the utility of parametric ARCH models in describing time-varying volatility in this
market. The parameters proxying for asymmetry in models that recognize the asymmetric behaviour of
volatility are highly significant in each and every case. However, the 'performance' of the various
parameterizations is often fairly similar with the exception of the multiplicative GARCH model that
performs qualitatively differently on several dimensions of performance. The outperformance of any
model(s) is not consistent across different sub-periods of the sample, suggesting that the optimal choice of a
model is period-specific. The outperformance is also not consistent as we change from in-sample inferences
to out-of-sample inferences within the same period. Copyright O 2000 John Wiley & Sons, Ltd.

1. INTRODUCTION
There is extensive empirical evidence that stock market volatility varies systematically with time.
The evidence dates back to the pioneering studies of Mandelbrot (1963) and Fama (1965) who
found that large price changes tend to be followed by large price changes and small price changes
by small price changes. More recent evidence is provided by Poterba and Summers (1986),
French et al. (1987), Chou (1988) and Schwert (1990).
There is also strong evidence that ARCH models are good descriptions of this time-varying
volatility in stock returns. Review articles such as Bollerslev et al. (1992) document the effective
application of ARCH models to financial time series across a wide variety of markets.' Examples
where significant ARCH effects are documented include Engle and Mustafa (1992) for individual
US stocks, Akgiray (1989) for US stock indices, Poon and Taylor (1992) for a UK stock index,
Corhay and Rad (1991) for a selection of international stock indices and Frennberg and Hansson
(1992) for the Swedish stock market.