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CYCLOCOPULA TECHNIQUE TO STUDY THE RELATIONSHIP BETWEEN TWO CYCLOSTATIONARY TIME SERIES WITH FRACTIONAL BROWNIAN MOTION ERRORS

MOHAMMAD REZA MAHMOUDI

Department of Statistics, Faculty of Science, Fasa University, Fasa, Fars, Iran

E-mail Address: mahmoudi.m.r@fasau.ac.ir

Corresponding author.

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and

AMIR MOSAVI

Faculty of Civil Engineering, Technische, Universität Dresden, 01069 Dresden, Germany

Institute of Software Design and Development, Óbuda University, 1034 Budapest, Hungary

Institute of Information Society, University of Public Service, 1083 Budapest, Hungary

Institute of Information Engineering, Automation and Mathematics, Slovak University of Technology in Bratislava, Bratislava, Slovakia

E-mail Address: amir.mosavi@mailbox.tu-dresden.de

Corresponding author.

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https://doi.org/10.1142/S0218348X22401375Cited by:3 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal AI-Based Analyses and Applications to Complex Systems: Part III
Lead Guest Editors: Yeliz Karaca & Dumitru Baleanu
Guest Editors: Majaz Moonis, Yu-Dong Zhang & Osvaldo Gervasi

Abstract

Detection of relationship between two time series is so important in different scientific fields. Most common techniques are usually sensitive to stationarity or normality assumptions. In this research, a new copula-based method (cyclocopula) is introduced to detect the relationship between two cylostationary time series with fractional Brownian motion (fBm) errors. The performance of the proposed method is studied by employing numerous simulated datasets. The applicability of the introduced approach is also investigated in real-world problems. The numerical and applied studies verify the performance of the introduced technique.

Keywords:

References

1. Q. Li, P. He, Y. He, X. Han, T. Zeng, G. Lu and H. Wang, Investigation to the relation between meteorological drought and hydrological drought in the upper Shaying River Basin using wavelet analysis, Atmos. Res. 234 (2020) 104743. Crossref, Web of Science, Google Scholar
2. T. R. Petty and P. Dhingra, Streamflow hydrology estimate using machine learning (SHEM), J. Am. Water Resour. Assoc. 54 (2018) 55–68. Crossref, Web of Science, Google Scholar
3. J. Liang, Q. Meng, X. Li, Y. Yuan, Y. Peng, X. Li, S. Li, Z. Zhu and M. Yan, The influence of hydrological variables, climatic variables and food availability on Anatidae in interconnected river-lake systems, the middle and lower reaches of the Yangtze River floodplain, Sci. Total Environ. 768 (2021) 144534. Crossref, Web of Science, Google Scholar
4. M. Peña-Gallardo, S. M. Vicente-Serrano, J. Hannaford, J. Lorenzo-Lacruz, M. Svoboda, F. Domínguez-Castro, M. Maneta, M. Tomas-Burguera and A. El Kenawy, Complex influences of meteorological drought time-scales on hydrological droughts in natural basins of the contiguous Unites States, J. Hydrol. 568 (2019) 611–625. Crossref, Web of Science, Google Scholar
5. S. Mirzaee, S. Yousefi, S. Keesstra, H. R. Pourghasemi, A. Cerdà and I. C. Fuller, Effects of hydrological events on morphological evolution of a fluvial system, J. Hydrol. 563 (2018) 33–42. Crossref, Web of Science, Google Scholar
6. X. Ablat, G. Liu, Q. Liu and C. Huang, Application of Landsat derived indices and hydrological alteration matrices to quantify the response of floodplain wetlands to river hydrology in arid regions based on different dam operation strategies, Sci. Total Environ. 688 (2019) 1389–1404. Crossref, Web of Science, Google Scholar
7. G. Konapala, S. C. Kao and N. Addor, Exploring hydrologic model process connectivity at the continental scale through an information theory approach, Water Resour. Res. 56(10) (2020) e2020WR027340. Crossref, Web of Science, Google Scholar
8. Y. Xu, X. Zhang, X. Wang, Z. Hao, V. P. Singh and F. Hao, Propagation from meteorological drought to hydrological drought under the impact of human activities: A case study in northern China, J. Hydrol. 579 (2019) 124147. Crossref, Web of Science, Google Scholar
9. C. Juez, D. Peña-Angulo, M. Khorchani, D. Regüés and E. Nadal-Romero, 20-years of hindsight into hydrological dynamics of a mountain forest catchment in the Central Spanish Pyrenees, Sci. Total Environ. 766 (2021) 142610. Crossref, Web of Science, Google Scholar
10. X. Tai, W. R. Anderegg, P. D. Blanken, S. P. Burns, L. Christensen and P. D. Brooks, Hillslope hydrology influences the spatial and temporal patterns of remotely sensed ecosystem productivity, Water Resour. Res. 56(11) (2020) e2020WR027630. Crossref, Web of Science, Google Scholar
11. J. Mallick, S. Talukdar, M. Alsubih, R. Salam, M. Ahmed, N. B. Kahla and M. Shamimuzzaman, Analysing the trend of rainfall in Asir region of Saudi Arabia using the family of Mann-Kendall tests, innovative trend analysis, and detrended fluctuation analysis, Theor. Appl. Climatol. 143(1) (2021) 823–841. Crossref, Web of Science, Google Scholar
12. J. Chen, C. Li, F. P. Brissette, H. Chen, M. Wang and G. R. Essou, Impacts of correcting the inter-variable correlation of climate model outputs on hydrological modeling, J. Hydrol. 560 (2018) 326–341. Crossref, Web of Science, Google Scholar
13. D. Myronidis, K. Ioannou, D. Fotakis and G. Dörflinger, Streamflow and hydrological drought trend analysis and forecasting in Cyprus, Water Resour. Manag. 32(5) (2018) 1759–1776. Crossref, Web of Science, Google Scholar
14. N. S. Abeysingha, M. G. Wickramasuriya and T. J. Meegastenna, Assessment of meteorological and hydrological drought; a case study in Kirindi Oya river basin in Sri Lanka, Int. J. Hydrol. Sci. Technol. 10(5) (2020) 429–447. Crossref, Google Scholar
15. I. Atif, J. Iqbal and M. A. Mahboob, Investigating snow cover and hydrometeorological trends in contrasting hydrological regimes of the Upper Indus basin, Atmosphere 9(5) (2018) 162. Crossref, Web of Science, Google Scholar
16. S. Wang, K. Zhang, L. P. H. van Beek, X. Tian and T. A. Bogaard, Physically-based landslide prediction over a large region: Scaling low-resolution hydrological model results for high-resolution slope stability assessment, Environ. Model. Softw. 124 (2020) 104607. Crossref, Web of Science, Google Scholar
17. S. B. Seo, R. D. Bhowmik, A. Sankarasubramanian, G. Mahinthakumar and M. Kumar, The role of cross-correlation between precipitation and temperature in basin-scale simulations of hydrologic variables, J. Hydrol. 570 (2019) 304–314. Crossref, Web of Science, Google Scholar
18. J. Dong, L. Wei, X. Chen, Z. Duan and Y. Lu, An instrument variable based algorithm for estimating cross-correlated hydrological remote sensing errors, J. Hydrol. 581 (2020) 124413. Crossref, Web of Science, Google Scholar
19. Y. R. Liu, Y. P. Li, Y. Ma, Q. M. Jia and Y. Y. Su, Development of a Bayesian-copula-based frequency analysis method for hydrological risk assessment — The Naryn River in Central Asia, J. Hydrol. 580 (2020) 124349. Crossref, Web of Science, Google Scholar
20. L. Ni, D. Wang, J. Wu, Y. Wang, Y. Tao, J. Zhang, J. Liu and F. Xie, Vine copula selection using mutual information for hydrological dependence modeling, Environ. Res. 186 (2020) 109604. Crossref, Web of Science, Google Scholar
21. V. Poonia, S. Jha and M. K. Goyal, Copula based analysis of meteorological, hydrological and agricultural drought characteristics across Indian river basins, Int. J. Climatol. 41 (2021) 4637–4652. Crossref, Web of Science, Google Scholar
22. M. N. Tahroudi, Y. Ramezani, C. De Michele and R. Mirabbasi, A new method for joint frequency analysis of modified precipitation anomaly percentage and streamflow drought index based on the conditional density of copula functions, Water Resour. Manag. 34(13) (2020) 4217–4231. Crossref, Web of Science, Google Scholar
23. Y. Fan, K. Huang, G. H. Huang and Y. P. Li, A factorial Bayesian copula framework for partitioning uncertainties in multivariate risk inference, Environ. Res. 183 (2020) 109215. Crossref, Web of Science, Google Scholar
24. F. Wang, Z. Wang, H. Yang, D. Di, Y. Zhao and Q. Liang, A new copula-based standardized precipitation evapotranspiration streamflow index for drought monitoring, J. Hydrol. 585 (2020) 124793. Crossref, Web of Science, Google Scholar
25. M. Sklar, Fonctions de repartition an dimensions et leurs marges, Publ. Inst. Stat. Univ. Paris, Inst. Henri Poincaré 8 (1959) 229–231. Google Scholar
26. R. B. Nelson, An Introduction to Copulas (Springer, New York, 2006). Google Scholar
27. B. Schweizer, Thirty years of copulas, in Advances in Probability Distributions with Given Marginals, Mathematics and Its Applications, Vol. 67 (Springer, Dordrecht, 1991), pp. 13–50. Crossref, Google Scholar
28. G. Masarotto and C. Varin, Gaussian copula marginal regression, Electron. J. Stat. 6 (2012) 1517–1549. Crossref, Web of Science, Google Scholar
29. E. J. Gumbel, Copula distribution des valeurs extremes en plusieurs dimensions in finance, Publ. Inst. Stat. Univ. Paris, Inst. Henri Poincaré 9 (1960) 171–173. Google Scholar
30. D. G. Clayton, A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika 65(1) (1978) 141–151. Crossref, Web of Science, Google Scholar
31. S. Demarta and A. J. McNeil, The $t$ $t$ copula and related copulas, Int. Stat. Rev. 73(1) (2005) 111–129. Crossref, Web of Science, Google Scholar
32. M. J. Frank, On the simultaneous associativity of $F (x, y)$ $F (x, y)$ and $x + y - F (x, y)$ $x + y - F (x, y)$ , Aequ. Math. 19 (1979) 194–226, https://eudml.org/doc/136825. Crossref, Google Scholar
33. A. R. Nematollahi, A. R. Soltani and M. R. Mahmoudi, Periodically correlated modeling by means of the periodograms asymptotic distributions, Stat. Pap. 58(4) (2017) 1267–1278. Crossref, Web of Science, Google Scholar
34. M. R. Mahmoudi and M. Maleki, A new method to detect periodically correlated structure, Comput. Stat. 32(4) (2017) 1569–1581. Crossref, Web of Science, Google Scholar
35. M. H. Heydari, M. R. Mahmoudi, A. Shakiba and A. Avazzadeh, Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion, Commun. Nonlinear Sci. Numer. Simul. 64 (2018) 98–121. Crossref, Web of Science, Google Scholar
36. M. H. Heydari, A. Avazzadeh and M. R. Mahmoudi, Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion, Chaos Solitons Fractals 124 (2019) 105–124. Crossref, Web of Science, Google Scholar
37. R Core Team, A language and environment for statistical computing (2015), R Foundation for Statistical Computing, Vienna, Austria, February 10, https://www.R-project.org/. Google Scholar
38. A. R. Zarei and M. R. Mahmoudi, Evaluation of changes in RDIst index effected by different Potential Evapotranspiration calculation methods, Water Resour. Manag. 31(15) (2017) 4981–4999. Crossref, Web of Science, Google Scholar
39. A. R. Zarei, M. M. Moghimi and M. R. Mahmoudi, Analysis of changes in spatial pattern of drought using RDI Index in south of Iran, Water Resour. Manag. 30(11) (2016) 3723–3743. Crossref, Web of Science, Google Scholar
40. A. R. Zarei, M. M. Moghimi and M. R. Mahmoudi, Parametric and non-parametric trend of drought in arid and semi-arid regions using RDI index, Water Resour. Manag. 30(14) (2016) 5479–5500. Crossref, Web of Science, Google Scholar

Vol. 30, No. 05

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History

Received 15 July 2021

Accepted 23 November 2021

Published: May 25, 2022

Information

This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part III”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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CYCLOCOPULA TECHNIQUE TO STUDY THE RELATIONSHIP BETWEEN TWO CYCLOSTATIONARY TIME SERIES WITH FRACTIONAL BROWNIAN MOTION ERRORS

Abstract

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