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dc.contributor.authorDeo, Rohit-
dc.contributor.authorHurvich, Clifford M.-
dc.contributor.authorSoulier, Philippe-
dc.contributor.authorWang, Yi-
dc.date.accessioned2008-05-25T15:27:10Z-
dc.date.available2008-05-25T15:27:10Z-
dc.date.issued2005-11-08-
dc.identifier.urihttp://hdl.handle.net/2451/26314-
dc.description.abstractWe establish sufficient conditions on durations that are stationary with finite variance and memory parameter d 2 [0; 1=2) to ensure that the corresponding counting process N(t) satisfies VarN(t) » Ct2d+1 (C > 0) as t ! 1, with the same memory parameter d 2 [0; 1=2) that was assumed for the durations. Thus, these conditions ensure that the memory in durations propagates to the same memory parameter in counts and therefore in realized volatility. We then show that any Autoregressive Conditional Duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, while any Long Memory Stochastic Duration model with d > 0 and all finite moments yields long memory in counts, with the same d. Finally, we present a result implying that the only way for a series of counts aggregated over a long time period to have nontrivial autocorrelation is for the short-term counts to have long memory. In other words, aggregation ultimately destroys all autocorrelation in counts, if and only if the counts have short memory.en
dc.languageEnglishEN
dc.language.isoen_USen
dc.publisherStern School of Business, New York Universityen
dc.relation.ispartofseriesSOR-2005-5en
dc.subjectLong Memory Stochastic Durationen
dc.subjectAutoregressive Conditional Durationen
dc.subjectRosenthal type Inequalityen
dc.titlePropagation of Memory Parameter from Durations to Countsen
dc.typeWorking Paperen
dc.description.seriesStatistics Working Papers SeriesEN
Appears in Collections:IOMS: Statistics Working Papers

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