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The memory of volatility

Faculty of Economics and Management, Leibniz University Hannover, Königsworther Platz 1, 30167 Hannover, Germany

Special Issue: Volatility of Prices of Financial Assets

The focus of the volatility literature on forecasting and the predominance of theconceptually simpler HAR model over long memory stochastic volatility models has led to the factthat the actual degree of memory estimates has rarely been considered. Estimates in the literaturerange roughly between 0.4 and 0.6 - that is from the higher stationary to the lower non-stationaryregion. This difference, however, has important practical implications - such as the existence or nonexistenceof the fourth moment of the return distribution. Inference on the memory order is complicatedby the presence of measurement error in realized volatility and the potential of spurious long memory.In this paper we provide a comprehensive analysis of the memory in variances of international stockindices and exchange rates. On the one hand, we find that the variance of exchange rates is subject tospurious long memory and the true memory parameter is in the higher stationary range. Stock indexvariances, on the other hand, are free of low frequency contaminations and the memory is in the lowernon-stationary range. These results are obtained using state of the art local Whittle methods that allowconsistent estimation in presence of perturbations or low frequency contaminations.
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© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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