SUMMARYThis paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications and inference methods, and identifies likely directions of future research.

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Opening, lunch and closing of financial markets induce a periodic component in the volatility of high-frequency returns. We show that price jumps cause a large bias in the classical periodicity estimators and propose robust alternatives. We find that accounting for periodicity greatly improves the accuracy of intraday jump detection methods. It increases the power to detect the relatively small jumps occurring at times for which volatility is periodically low and reduces the number of spurious jump detections at times of periodically high volatility. We use the series of detected jumps to estimate robustly the long memory parameter of the squared EUR/USD, GBP/ USD and YEN/USD returns.