Introduction

Abstract

Financial returns, albeit unpredictable according to the definition of Sims (1984), display both temporal dependency in their second order moments and heavy-peaked and tailed distributions. While such a phenomenon was known at least since the pioneer work of Mandelbrot (1963) and Fama (1965), it was only with the introduction of the autoregressive conditionally heteroscedastic (ARCH) model of Engle (1982) and Bollerslev (1986) that econometric models of changing volatility have been intensively fitted to data. ARCH models have had a prominent role in the analysis of many aspects of financial econometrics, such as the term structure of interest rates, the pricing of options, the presence of time varying risk premia in the foreign exchange market: see Bollerslev et al. (1992), Bera and Higgins (1993), Bollerslev et al. (1994) or Palm (1996) for surveys. The quintessence of the ARCH model is to make volatility dependent on the variability of past observations. An alternative formulation initiated by Taylor (1986) makes volatility be driven by unobserved components, and has come to be known as the stochastic volatility (SV) model. As for the ARCH models, SV models have also been intensively used in the last decade, especially after the progress accomplished in the corresponding estimation techniques, as illustrated in the excellent surveys of Ghysels et al. (1996) and Shephard (1996). Early contributions that aimed at relating changes in volatility of asset returns to economic intuition include Clark (1973) and Tauchen and Pitts (1983), who assumed that a stochastic process of information arrival generates a random number of intraday changes of the asset price.