Applied and Computational Mathematics
Volume 8, Issue 2, April 2019, Pages: 44-49
Received: Jul. 4, 2019;
Published: Jul. 29, 2019
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Lai Simin, School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Wan Li, School of Mathematics and Information Science, Guangzhou University, Guangzhou, China; Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, China
Zeng Xiangjian, School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Data missing often affects the characteristics of the sequence. Using appropriate methods to process the missing data is the premise and guarantee to obtain high quality information. In this study, a fractal interpolation method is proposed to fill the missing data with self-similar feature sequences. Two sets of binomial multifractal sequences with parameters of 0.25 and 0.35 are taken as the research objects, and the Hurst index value of the sequence after filling processing is calculated by MF-DMA, which verifies the practicability of the fractal interpolation filling method. At the same time, the method is applied to multi-fractal sequences with missing rates of 10%, 15% and 20% respectively, and compared with the filling effects of deletion method and random filling method, then, the applicability of the three methods is obtained. The results show that, for binomial multifractal sequences with different missing ratios, the Hurst index of the sequence processed by fractal interpolation has the highest degree of fitting with the theoretical value, its effect of repairing the fractal sequence is better than the other two methods, and has a good application prospect.
Comparative Analysis of Multi-fractal Data Missing Processing Methods, Applied and Computational Mathematics.
Vol. 8, No. 2,
2019, pp. 44-49.
Rubin D B. Multiple Imputation for Nonresponse in Surveys [M]. John Wiley, 1987.
Mao Qunxia, Li Xiaosong. Comparison of Multiple Filling Method and Ad Hoc Method for Processing Missing Values in Simulated Longitudinal Data Sets [J]. Modern Preventive Medicine, 2005 (04): 310-312.
Tan H, Feng G, Feng J, et al. A tensor-based method for missing traffic data completion [J]. Transportation Research Part C: Emerging Technologies, 2013, 28: 15-27.
Dohoo I R. Dealing with deficient and missing data.[J]. Preventive Veterinary Medicine, 2015, 122 (1-2): 221-228.
Xia Liling, Zhu Yuelong. Optimizing the method of water environment data missing processing [J]. Hydropower and Energy Science, 2018, 36 (04): 158-161+85.
Bouchaud J P, Potters M, Meyer M. Apparent multifractality in financial time series [J]. The European Physical Journal, 2000, 13 (3): 595-599.
Chen Peng, Zheng Manxian. Multifractal Characteristics and Conduction Effect of International Commodity Price Fluctuation [J]. Price Theory and Practice, 2018 (10): 81-84.
Zhang Yong, Guan Wei. Multifractal Analysis of Traffic Flow Time Series [J]. Computer Engineering and Applications, 2010, 46 (29): 23-25.
Chen Y, Xiang Z, Dong Y, et al. Multi-Fractal Characteristics of Mobile Node’s Traffic in Wireless Mesh Network with AODV and DSDV Routing Protocols [J]. Wireless Personal Communications, 2011, 58 (4): 741-757.
Gu G F, Zhou W X. Detrending moving average algorithm for multifractals [J]. Physical Review E. 2010, 82 (1): 011136.
Mali P. Multifractal detrended moving average analysis of global temperature records [J]. Journal of Statistical Mechanics Theory & Experiment, 2016, 2016 (1): 013201.
Li Q, Cao G, Xu W. Relationship research between meteorological disasters and stock markets based on a multifractal detrending moving average algorithm [J]. International Journal of Modern Physics B, 2018, 32 (01): 1.
Amo E D, Carrillo M D, Sánchez J F. PCF self-similar sets and fractal interpolation [J]. Mathematics & Computers in Simulation, 2013, 92 (6): 28-39.
Jiang P, Liu F, Wang J, Song Y. Cuckoo search-designated fractal interpolation functions with winner combination for estimating missing values in time series [J]. Applied Mathematical Modelling, 2016, 40 (23-24): 9692-9718.
Fu Y, Zheng Z, Xiao R, Shi H. Comparison of two fractal interpolation methods [J]. Physica A: Statistical Mechanics and its Applications, 2017, 469.
Kantelhardt J W, Zschiegner S A, Koscielny-Bunde E, et al. Multifractal detrended fluctuation analysis of nonstationary time series [J]. Physica A: Statistical Mechanics and its Applications, 2002.
Mali P, Mukhopadhyay A. Multifractal characterization of gold market: A multifractal detrended fluctuation analysis [J]. Physica A: Statistical Mechanics and its Applications, 2014, 413: 361-372.
Xie W J, Han R Q, Jiang Z Q, et al. Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures [J]. EPL (Europhysics Letters), 2017, 119 (4): 48008.