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WhenShouldTimebeContinuous?
Volatilitymodelingandestimationofhigh-frequencydata
Abstract:
Thepaperstudiestheproblemofvolatilitymodelingandestimationofhigh-frequency
ataundercontinuousrecordasymptotics.Theapproachdecomposestheobserveddatainto
ricedi?usionandstationarycomponents.Thedi?usioncomponentmaybeidenti?edas
e\true"valueoftheunderlyingasset.Thestationarycomponent,termedasthehigh-
equency\noise"(HFN),accommodatespertinentmarketmicrostructurefeatures.Asimple
ndition,characterizingtheHFNcomponentonwhichconventionalvolatilityestimatorson
ebasisofnoisyobservationswillbeconsistentfordi?usionvolatility,isderived,andis
ppliedtoReutersFXFXdata.Itisshownthatconventionalvolatilityestimatorsleadto
bstantialspuriousvolatilityinhigh-frequencyreturns.Thefailureofconventionalestima-
rsinprovidingconsistentestimatesisduetothehigherirregularitiesoftheHFNsample
ath,whichisinduced,atleastinpart,bytraderheterogeneity.Inaddition,theoptimal
mplingfrequencyisacquiredwhichjusti?estheappropriatenessoftheuseofthe10-to15-
inutesamplingintervals-thebenchmarknoise?lterusedinmanyrecentempiricalstudies
ealingwithhigh-frequencyforeignexchangedata.
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