The pervasive intraday periodicity in the return volatility in foreign exchange and equitymarkets is shown to have a strong impact on the dynamic properties of high frequencyreturns. Only by taking account of this strong intraday periodicity is it possible to uncoverthe complex intraday volatility dynamics that exists both within and across differentfinancial markets. The explicit periodic modeling procedure developed here provides such aframework and thus sets the stage for a formal integration of standard volatility models withmarket microstructure variables to allow for a more comprehensive empirical investigationof the fundamental determinants behind the volatility clustering phenomenon. c 1997Elsevier Science B.V.