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Multifractal theory with its applications in data management. (English) Zbl 1406.91301

Summary: The extraction of interesting information from enormous and irregular datasets has always been a significant research topic. For the datasets with irregular distribution and self-similarity, multifractal theory is the most appreciated approach and has been successfully applied in many fields, such as financial analysis, image processing, medical diagnosis, earthquake study, etc. In this paper, we make a detailed analysis and summary on three main functions, namely multifractal structure diagnosis, tendency and singularity analysis. Finally, some experiments based on oil prices data and spatial physical data are carried out to validate its performance effectively.

MSC:

91B82 Statistical methods; economic indices and measures
91G80 Financial applications of other theories
28A80 Fractals
86A25 Geo-electricity and geomagnetism
62P20 Applications of statistics to economics
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