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We investigate the time series properties of a volatility model, whose conditional variance is specified as
in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated
or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility
functions. In the paper, such a model is shown to generate many important characteristics that are
commonly observed in financial time series. In particular, the model yields persistence in volatility,
and also well predicts leptokurtosis. This is true for any type of volatility functions considered in the
paper, as long as the covariate is integrated or nearly integrated. Stationary covariates cannot produce
important characteristics observed in many financial time series. We present two empirical applications
of the model, which show that the default premium (the yield spread between Baa and Aaa corporate
bonds) affects stock return volatility and the interest rate differential between two countries accounts
for exchange rate return volatility. The forecast evaluation shows that the model generally outperforms
GARCH and FIGARCH at relatively lower frequencies.
Published by Elsevier B.V.