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    Testing Self-Similarity Through Lamperti Transformations

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    Type
    Article
    Authors
    Lee, Myoungji
    Genton, Marc G. cc
    Jun, Mikyoung
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2016-07-14
    Online Publication Date
    2016-07-14
    Print Publication Date
    2016-09
    Permanent link to this record
    http://hdl.handle.net/10754/621509
    
    Metadata
    Show full item record
    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.
    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.
    Sponsors
    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).
    Publisher
    Springer Nature
    Journal
    Journal of Agricultural, Biological, and Environmental Statistics
    DOI
    10.1007/s13253-016-0258-1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s13253-016-0258-1
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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