Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionStatistics Program
KAUST Grant Number
KUS-C1-016-04Date
2016-07-14Online Publication Date
2016-07-14Print Publication Date
2016-09Permanent link to this record
http://hdl.handle.net/10754/621509
Metadata
Show full item recordAbstract
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 Natureae974a485f413a2113503eed53cd6c53
10.1007/s13253-016-0258-1