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dc.contributor.authorLee, Myoungji
dc.contributor.authorGenton, Marc G.
dc.contributor.authorJun, Mikyoung
dc.date.accessioned2016-11-03T08:31:03Z
dc.date.available2016-11-03T08:31:03Z
dc.date.issued2016-07-14
dc.identifier.citationLee M, Genton MG, Jun M (2016) Testing Self-Similarity Through Lamperti Transformations. JABES 21: 426–447. Available: http://dx.doi.org/10.1007/s13253-016-0258-1.
dc.identifier.issn1085-7117
dc.identifier.issn1537-2693
dc.identifier.doi10.1007/s13253-016-0258-1
dc.identifier.urihttp://hdl.handle.net/10754/621509
dc.description.abstractSelf-similar processes have been widely used in modeling real-world phenomena occurring in environmetrics, network traffic, image processing, and stock pricing, to name but a few. The estimation of the degree of self-similarity has been studied extensively, while statistical tests for self-similarity are scarce and limited to processes indexed in one dimension. This paper proposes a statistical hypothesis test procedure for self-similarity of a stochastic process indexed in one dimension and multi-self-similarity for a random field indexed in higher dimensions. If self-similarity is not rejected, our test provides a set of estimated self-similarity indexes. The key is to test stationarity of the inverse Lamperti transformations of the process. The inverse Lamperti transformation of a self-similar process is a strongly stationary process, revealing a theoretical connection between the two processes. To demonstrate the capability of our test, we test self-similarity of fractional Brownian motions and sheets, their time deformations and mixtures with Gaussian white noise, and the generalized Cauchy family. We also apply the self-similarity test to real data: annual minimum water levels of the Nile River, network traffic records, and surface heights of food wrappings. © 2016, International Biometric Society.
dc.description.sponsorshipThis work was partially supported by NSF Grant DMS-1208421 and Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
dc.publisherSpringer Nature
dc.subjectFractional Brownian sheet
dc.titleTesting Self-Similarity Through Lamperti Transformations
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.identifier.journalJournal of Agricultural, Biological, and Environmental Statistics
dc.contributor.institutionInstitute for Applied Mathematics and Computational Science, Texas A&M University, College Station, TX, United States
dc.contributor.institutionDepartment of Statistics, Texas A&M University, College Station, TX, United States
kaust.personGenton, Marc G.
kaust.grant.numberKUS-C1-016-04
dc.date.published-online2016-07-14
dc.date.published-print2016-09


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