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The pervasive intraday periodicity in the return volatility in foreign exchange and equity markets is shown to have a strong impact on the dynamic properties of high frequency returns. Only by taking account of this strong intraday periodicity is it possible to uncover the complex intraday volatility dynamics that exists both within and across different financial markets. The explicit periodic modeling procedure developed here provides such a framework and thus sets the stage for a formal integration of standard volatility models with market microstructure variables to allow for a more comprehensive empirical investigation of the fundamental determinants behind the volatility clustering phenomenon.