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On the distinction between fractal and seasonal dependencies in time series data. (English) Zbl 07468068

MSC:

62-XX Statistics
86-XX Geophysics

Software:

longmemo; TSA; ltsa
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References:

[1] Brown, C. and Liebovitch, L., Fractal Analysis, , Vol. 165 (Sage, Thousand Oaks, CA, 2010).
[2] Kaplan, D. and Glass, L., Understanding Nonlinear Dynamics (Springer, New York, 1995). · Zbl 0823.34002
[3] Lauwerier, H., Fractals: Endlessly Repeated Geometrical Figures (Princeton University Press, Princeton, NJ, 1991). · Zbl 0765.58002
[4] Mandelbrot, B. B., The Fractal Geometry of Nature (McMillan, New York, 1983).
[5] Bak, P., How Nature Works: The Science of Self-Organized Criticality (Springer, New York, 1996). · Zbl 0894.00007
[6] Feder, J., Fractals (Plenum Press, New York, 1988). · Zbl 0648.28006
[7] Peng, C. K., Mietus, J., Hausdorff, J. M., Havlin, S., Stanley, H. E. and Goldberger, A. L., Long-range anti-correlations and non-Gaussian behavior of the heartbeat, Phys. Rev. Lett.70 (1993) 1343-1346.
[8] Van Orden, G. C., Holden, J. G. and Turvey, M. T., Human cognition and \(1/f\) scaling, J. Exp. Psychol.134(1) (2005) 117-123.
[9] Aks, D. J. and Sprott, J. C., The role of depth and \(1/f\) dynamics in perceiving reversible figures, Nonlinear Dyn. Psychol. Life Sci.7 (2003) 161-180. · Zbl 1201.91171
[10] Chen, Y., Ding, M. and Kelso, J. A., Long memory processes \((1/ f^\alpha\) type) in human coordination, Phys. Rev. Lett.79(22) (1997) 4501-4504.
[11] Box-Steffensmeier, J. M. and Smith, R. M., Investigating political dynamics using fractional integration methods, Am. J. Polit. Sci.42(2) (1998) 661-689.
[12] Eisinga, R., Franses, P. H. and Ooms, M., Forecasting long memory left-right political orientations, Int. J. Forecast.15(2) (1999) 185-199.
[13] Koopmans, M., A dynamical view of high school attendance: An assessment of short-term and long-term dependencies in five urban schools, Nonlinear Dyn. Psychol. Life Sci.19(1) (2015) 65-80.
[14] Koopmans, M., On the pervasiveness of long range memory processes in daily high school attendance rates.Nonlinear Dyn. Psychol. Life Sci.22(2) (2018) 243-262.
[15] Mandelbrot, B. B., Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (Springer, New York, 1997). · Zbl 1005.91001
[16] Sowell, F., Modeling long-run behavior with the fractional ARFIMA model, J. Monet. Econ.29(2) (1992) 277-302.
[17] Stadnitski, T., Measuring fractality, Front. Physiol.3 (2012) 127.
[18] Kauffman, S. A., The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, New York, 1993).
[19] Delignières, D., Torre, K. and Lemoine, L., Methodological issues in the application of monofractal analysis in psychological and behavioral research, Nonlinear Dyn. Psychol. Life Sci.9 (2005) 435-461.
[20] Taqqu, M. S., Teverovsky, V. and Willinger, W., Estimators of long-range dependence: An empirical study, Fractals3(4) (1995) 785-803. · Zbl 0864.62061
[21] Stadnytska, T., Braun, S. and Werner, J., Analyzing fractal dynamics employing R, Nonlinear Dyn. Psychol. Life Sci.14(2) (2010) 117-144.
[22] Higuchi, T., Approach to an irregular time series on the basis of the fractal theory, Physica D31 (1988) 277-283. · Zbl 0649.58046
[23] Granger, C. W. J. and Joyeux, R., An introduction to long-memory time series models and fractional differencing, J. Time Ser. Anal.1(1) (1980) 15-29. · Zbl 0503.62079
[24] Eke, A., Hermán, P., Bassingthwaighte, J. B., Raymond, G. M., Perival, D. B., Cannon, M., Balla, I. and Ikrényi, C., Physiological time series: Distinguishing fractal noises from motions, Pflügers Arch.439 (2000) 402-415.
[25] Hurst, H. E., The problem of long-term storage in reservoirs, Hydrol. Sci.1(3) (1956) 13-27, https://doi.org/10.1080/02626665609493644.
[26] Koopmans, M., Using Time Series to Analyze Long-Range Fractal Patterns, , Vol. 185 (Sage, Thousand Oaks, CA, 2021).
[27] Box, G. and Jenkins, G., Time Series Analysis: Forecasting and Control (Holden-Day, San Francisco, 1970). · Zbl 0249.62009
[28] Beran, J., Statistics for Long-Memory Processes (Chapman-Hall, New York, 1994). · Zbl 0869.60045
[29] Stadnitski, T., Some critical aspects of fractality research, Nonlinear Dyn. Psychol. Life Sci.16(2) (2012) 137-158.
[30] Cryer, J. D. and Chan, K. S., Time Series Analysis: With Applications in R, 2nd edn. (Springer, New York, 2008). · Zbl 1137.62366
[31] Shumway, R. H. and Stoffer, D. S., Time Series and Its Applications, 3rd edn. (Springer, New York, 2011). · Zbl 1276.62054
[32] Bloomfield, P., Fourier Analysis for Time Series: An Introduction (Wiley, New York, 1976). · Zbl 0353.62051
[33] Stadnitski, T., in The Fractal Geometry of the Brain, ed. Di Leva, A. (Springer, New York, 2016).
[34] Geweke, J. and Porter-Hudak, S., The estimation and application of long memory in time series models, J. Time Ser. Anal.4(4) (1983) 221-238. · Zbl 0534.62062
[35] Reisen, V. A., Estimation of the fractional difference parameter in the ARFIMA \((pdq)\) model using the smoothed periodogram, J. Time Ser. Anal.15(3) (1994) 335-350. · Zbl 0803.62084
[36] Clarke, H. D. and Lebo, M., Fractional (co)integ-ration and governing part support in Britain, Br. J. Polit. Sci.33 (2003) 283-301.
[37] McLeod, A. I., Yu, H. and Krougly, Z. L., Algorithms for linear time series analysis: With R package, J. Stat. Softw.23(5) (2007) 1-26.
[38] Hamilton, P., Pollock, J. E., Mitchell, D. A., Vincenzi, A. E. and West, B. J., The application of nonlinear dynamics to nursing research, Nonlinear Dyn. Psychol. Life Sci.1 (1997) 237-261.
[39] Said, S. E. and Dickey, D. A., Testing for unit roots in autoregressive—Moving average models of unknown order, Biometrika71 (1984) 599-608. · Zbl 0564.62075
[40] Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y., Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?J. Econom.54 (1992) 159-178. · Zbl 0871.62100
[41] Wijnants, M. L., Cox, R. F. A., Hasselman, F., Bosman, A. M. T. and Van Orden, G., Does sample rate introduce an artifact in spectral analysis of continuous processes?Front. Physiol.3 (2012) 495, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549522/.
[42] M. Demetrescu and U. Hassler, Effect of neglected deterministic seasonality on unit root tests, Stat. Papers48 (2007) 385-402. · Zbl 1125.62099
[43] Porter-Hudak, S., An application of the seasonal fractionally differenced model to the monetary aggregates, J. Am. Stat. Assoc.85(410) (1990) 338-344.
[44] J. Q. Veenstra, Persistence and anti-persistence: Theory and software, Doctoral Dissertation, Electronic Thesis and Dissertation Repository, Western University, (2013), Paper 1119.
[45] Wagenmakers, E. J., Farrell, S. and Ratcliff, R., Estimation and interpretation of \(1/ f^\alpha\) noise in human cognition, Psych. Bull. Rev.11(4) (2004) 579-615.
[46] Taqqu, M. S. and Teverovksy, V., in A Practical Guide to Heavy Tails, eds. Adler, R., Feldman, R. B. and Taqqu, M. S. (Birkhauser, Boston, 1997).
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