{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T12:53:17Z","timestamp":1676811197101},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2002,9,24]],"date-time":"2002-09-24T00:00:00Z","timestamp":1032825600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:p>We consider the asymptotic behavior of log-periodogram regression \nestimators of the memory parameter in long-memory stochastic \nvolatility models, under the null hypothesis of short memory \nin volatility. We show that in this situation, if the periodogram \nis computed from the log squared returns, then the estimator \nis asymptotically normal, with the same asymptotic mean and \nvariance that would hold if the series were Gaussian. In \nparticular, for the widely used GPH estimator \n[d with circumflex above]<jats:sub><jats:italic>GPH<\/jats:italic><\/jats:sub> under the null hypothesis, \nthe asymptotic mean of \n<jats:italic>m<\/jats:italic><jats:sup>1\/2<\/jats:sup>[d with circumflex above]<jats:sub><jats:italic>GPH<\/jats:italic><\/jats:sub> \nis zero and the asymptotic variance is \u03c0<jats:sup>2<\/jats:sup>\/24 where \n<jats:italic>m<\/jats:italic> is the number of Fourier frequencies used in the regression. \nThis justifies an ordinary Wald test for long memory in volatility based \non the log periodogram of the log squared returns.<\/jats:p>","DOI":"10.1017\/s0266466602186014","type":"journal-article","created":{"date-parts":[[2008,4,21]],"date-time":"2008-04-21T10:47:01Z","timestamp":1208774821000},"page":"1291-1308","source":"Crossref","is-referenced-by-count":13,"title":["TESTING FOR LONG MEMORY IN VOLATILITY"],"prefix":"10.1017","volume":"18","author":[{"given":"Clifford M.","family":"Hurvich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Soulier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2002,9,24]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466602186014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:18:51Z","timestamp":1557188331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466602186014\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9,24]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["S0266466602186014"],"URL":"https:\/\/doi.org\/10.1017\/s0266466602186014","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9,24]]}}}