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A computational technique to classify several fractional Brownian motion processes

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  • Mahmoudi, Mohammad Reza

Abstract

In this paper, for the first time, the classification of several fractional Brownian motion time series is considered. For this purpose, fuzzy clustering technique is applied and Brownian motion processes are classified. The applicability of the given approach is explored using simulated and a real COVID-19 dataset.

Suggested Citation

  • Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921005063
    DOI: 10.1016/j.chaos.2021.111152
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    1. Umberto Triacca, 2016. "Measuring the Distance between Sets of ARMA Models," Econometrics, MDPI, vol. 4(3), pages 1-11, July.
    2. Mohammad Reza Mahmoudi & Mohammad Hossein Heydari & Zakieh Avazzadeh, 2019. "Testing the difference between spectral densities of two independent periodically correlated (cyclostationary) time series models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2320-2328, May.
    3. Carsten Jentsch, 2012. "A new frequency domain approach of testing for covariance stationarity and for periodic stationarity in multivariate linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 177-192, March.
    4. Maharaj, Elizabeth Ann, 2002. "Comparison of non-stationary time series in the frequency domain," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 131-141, July.
    5. Salcedo, Gladys E. & Porto, Rogério F. & Morettin, Pedro A., 2012. "Comparing non-stationary and irregularly spaced time series," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3921-3934.
    6. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June.
    7. Holger Dette & Efstathios Paparoditis, 2009. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 831-857, September.
    8. Mahmoudi, Mohammad Reza & Heydari, Mohammad Hossein & Roohi, Reza, 2019. "A new method to compare the spectral densities of two independent periodically correlated time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 103-110.
    9. Domenico Piccolo, 1990. "A Distance Measure For Classifying Arima Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(2), pages 153-164, March.
    10. Alonso, Andrés M. & Peña, Daniel & Romo, Juan, 2003. "On sieve bootstrap prediction intervals," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 13-20, October.
    11. Peter J. Diggle & Nicholas I. Fisher, 1991. "Nonparametric Comparison of Cumulative Periodograms," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(3), pages 423-434, November.
    12. B. M. Pötscher & E. Reschenhofer, 1988. "Discriminating Between Two Spectral Densities In Case Of Replicated Observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(3), pages 221-224, May.
    13. Alonso, A.M. & Berrendero, J.R. & Hernandez, A. & Justel, A., 2006. "Time series clustering based on forecast densities," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 762-776, November.
    14. Abdol Rassoul Zarei & Mohammad Reza Mahmoudi, 2017. "Evaluation of changes in RDIst index effected by different Potential Evapotranspiration calculation methods," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(15), pages 4981-4999, December.
    15. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2009. "Comparison of time series with unequal length in the frequency domain," MPRA Paper 15310, University Library of Munich, Germany.
    16. Jentsch, Carsten & Pauly, Markus, 2012. "A note on using periodogram-based distances for comparing spectral densities," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 158-164.
    17. Fruhwirth-Schnatter, Sylvia & Kaufmann, Sylvia, 2008. "Model-Based Clustering of Multiple Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 78-89, January.
    18. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    19. Timmer, J. & Lauk, M. & Vach, W. & Lucking, C. H., 1999. "A test for a difference between spectral peak frequencies," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 45-55, March.
    20. Abdol Rassoul Zarei & Mohammad Mehdi Moghimi & Mohammad Reza Mahmoudi, 2016. "Analysis of Changes in Spatial Pattern of Drought Using RDI Index in south of Iran," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(11), pages 3723-3743, September.
    21. Heydari, M.H. & Avazzadeh, Z. & Mahmoudi, M.R., 2019. "Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 105-124.
    22. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    23. Pattarin, Francesco & Paterlini, Sandra & Minerva, Tommaso, 2004. "Clustering financial time series: an application to mutual funds style analysis," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 353-372, September.
    24. Abdol Rassoul Zarei & Mohammad Mehdi Moghimi & Mohammad Reza Mahmoudi, 2016. "Parametric and Non-Parametric Trend of Drought in Arid and Semi-Arid Regions Using RDI Index," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(14), pages 5479-5500, November.
    25. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
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