Testing Self-Similarity Through Lamperti Transformations
dc.contributor.author | Lee, Myoungji | |
dc.contributor.author | Genton, Marc G. | |
dc.contributor.author | Jun, Mikyoung | |
dc.date.accessioned | 2016-11-03T08:31:03Z | |
dc.date.available | 2016-11-03T08:31:03Z | |
dc.date.issued | 2016-07-14 | |
dc.identifier.citation | Lee 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.issn | 1085-7117 | |
dc.identifier.issn | 1537-2693 | |
dc.identifier.doi | 10.1007/s13253-016-0258-1 | |
dc.identifier.uri | http://hdl.handle.net/10754/621509 | |
dc.description.abstract | Self-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.sponsorship | This 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.publisher | Springer Nature | |
dc.subject | Fractional Brownian sheet | |
dc.title | Testing Self-Similarity Through Lamperti Transformations | |
dc.type | Article | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.contributor.department | Statistics Program | |
dc.identifier.journal | Journal of Agricultural, Biological, and Environmental Statistics | |
dc.contributor.institution | Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, TX, United States | |
dc.contributor.institution | Department of Statistics, Texas A&M University, College Station, TX, United States | |
kaust.person | Genton, Marc G. | |
kaust.grant.number | KUS-C1-016-04 | |
dc.date.published-online | 2016-07-14 | |
dc.date.published-print | 2016-09 |
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