{"title":"Itô的漂移理论，赫斯特系数，和分数漂移在金融","authors":"Paitoon Wongsasutthikul, C. Turvey","doi":"10.2139/ssrn.2034472","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate how Ito’s excursion theory can be usefully applied to economic time series data (Ito 2007). We relate excursion theory to geometric and fractional Brownian motion and the Hurst coefficient. We then calculate the Hurst coefficient for all stocks on the DOW 30, S&P 500 and Russell 2000, showing the distribution of Hurst measures and relating them statistically to excursions. In doing so we provide a nice and intuitive link between Brownian motion and excursions, an application and consequence that we have not seen before.","PeriodicalId":242545,"journal":{"name":"ERN: Econometric Studies of Capital Markets (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Itô’s Excursion Theory, the Hurst Coefficient, and Fractional Excursions in Finance\",\"authors\":\"Paitoon Wongsasutthikul, C. Turvey\",\"doi\":\"10.2139/ssrn.2034472\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate how Ito’s excursion theory can be usefully applied to economic time series data (Ito 2007). We relate excursion theory to geometric and fractional Brownian motion and the Hurst coefficient. We then calculate the Hurst coefficient for all stocks on the DOW 30, S&P 500 and Russell 2000, showing the distribution of Hurst measures and relating them statistically to excursions. In doing so we provide a nice and intuitive link between Brownian motion and excursions, an application and consequence that we have not seen before.\",\"PeriodicalId\":242545,\"journal\":{\"name\":\"ERN: Econometric Studies of Capital Markets (Topic)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ERN: Econometric Studies of Capital Markets (Topic)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.2034472\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Econometric Studies of Capital Markets (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.2034472","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Itô’s Excursion Theory, the Hurst Coefficient, and Fractional Excursions in Finance
In this paper, we investigate how Ito’s excursion theory can be usefully applied to economic time series data (Ito 2007). We relate excursion theory to geometric and fractional Brownian motion and the Hurst coefficient. We then calculate the Hurst coefficient for all stocks on the DOW 30, S&P 500 and Russell 2000, showing the distribution of Hurst measures and relating them statistically to excursions. In doing so we provide a nice and intuitive link between Brownian motion and excursions, an application and consequence that we have not seen before.
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