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Data Series as a Source for Modelling

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Extracting Knowledge From Time Series

Part of the book series: Springer Series in Synergetics ((SSSYN))

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Abstract

When a model is constructed from “first principles”, its variables inherit the sense implied in those principles which can be general laws or derived equations, e.g., like Kirchhoff’s laws in the theory of electric circuits. When an empirical model is constructed from a time realisation, it is a separate task to reveal relationships between model parameters and object characteristics. It is not always possible to measure all variables entering model equations either in principle or due to technical reasons. So, one has to deal with available data and, probably, perform additional data transformations before constructing a model.

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Notes

  1. 1.

    For example, when e.m.f. is measured with a voltmeter, one can either allow for finiteness of R v or use a classical no-current compensatory technique with a potentiometer (Kalashnikov, 1970, pp. 162–163; Herman, 2008) which is free of the above shortcoming.

  2. 2.

    Thus, experiments show that in electric measurements (e.g., Fig. 6.2) a sensitive wideband device (e.g., a radio receiver) connected in parallel with a voltmeter or a cardiograph detects also noise, human speech and music, etc.

  3. 3.

    In the field of artificial neural networks, somewhat different terminology is accepted. A test series is a series used to compare different empirical models. It allows to select the best one among them. For the “honest” comparison of the best model with an object, one uses one more time series called a validation time series. A training time series is often called a learning sample. However, we follow the terminology described in the text above.

  4. 4.

    Not a power. Mean power equals zero in this case, since a signal must decay to zero at infinity to be integrable over the entire number axis.

  5. 5.

    Difference of Gaussians, i.e. Gauss functions.

  6. 6.

    Thus, a phase of a pendulum oscillations (Fig. 3.5a) can be changed by holding it back at a point of maximal deflection from an equilibrium state without energy consumption.

  7. 7.

    This narrow-band-gap semiconductor characterised by a large mobility of charge carriers is promising in respect of the increase in the operating speed of semiconductor devices.

  8. 8.

    Liquid nitrogen in a thermos is under boiling temperature. At a low heat flow from the sample, small bubbles arise at its surface. They cover the entire surface at a more intensive heating. Thus, a vapour film is created, which isolates the sample from the cooling liquid.

References

  • Afraimovich, V.S., Nekorkin, V.I., Osipov, G.V., Shalfeev, V.D.: Stability, structures, and chaos in nonlinear synchronisation networks. Gor’ky Inst. Appl. Phys. RAS, Gor’ky, (in Russian) (1989)

    Google Scholar 

  • Aivazian, S.A.: Statistical Investigation of Dependencies. Metallurgiya, Moscow, (in Russian) (1968)

    Google Scholar 

  • Anishchenko, V.S., Vadivasova, T.Ye.: Relationship between frequency and phase characteristics of chaos: two criteria of synchronization. J. Commun. Technol. Electron. 49(1), 69–75 (2004)

    Google Scholar 

  • Arnhold, J., Lehnertz, K., Grassberger, P., Elger, C.E.: A robust method for detecting interdependences: application to intracranially recorded EEG. Physica D. 134, 419–430 (1999)

    Article  ADS  MATH  Google Scholar 

  • Astaf’eva N.M.: Wavelet analysis: basic theory and some applications. Phys. Uspekhi. 39, 1085–1108 (1996)

    Article  ADS  Google Scholar 

  • Barenblatt, G.I.: Similarity, Self-similarity, Intermediate Asymptotics, Gidrometeoizdat, Leningrad (1982). Translated into English: Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  • Bezruhcko, B.P., Erastova, E.N.: About possibility of chaotic solutions in model of narrow-band-gap semiconductor in ionisation by collision regime. Sov. Phys. Semiconduct. 23(9), 1707–1709 (in Russian), (1989)

    Google Scholar 

  • Blekhman, I.I.: Synchronisation in Nature and Technology. Nauka, Moscow (1981). Translated into English: ASME Press, New York (1988)

    Google Scholar 

  • Blekhman, I.I.: Synchronisation of Dynamic Systems. Nauka, Moscow, (in Russian) (1971)

    Google Scholar 

  • Bloomfield, P.: Fourier Analysis of Time Series: An Introduction. Wiley, New York (1976)

    Google Scholar 

  • Boccaletti, S., Kurths, S., Osipov, G., Valladares, D., Zhou, C.: The synchronization of chaotic systems. Phys. Rep. 366, 1–52 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Box, G.E.P., Jenkins, G.M.: Time Series Analysis. Forecasting and Control. Holden-Day, San Francisco (1970)

    Google Scholar 

  • Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer, Berlin (1987)

    Google Scholar 

  • Brown, R., Rulkov, N.F., Tracy, E.R.: Modeling and synchronizing chaotic systems from experimental data. Phys. Lett. A. 194, 71–76 (1994)

    Article  ADS  Google Scholar 

  • Cecen, A.A., Erkal, C.: Distinguishing between stochastic and deterministic behavior in high frequency foreign exchange rate returns: Can non-linear dynamics help forecasting? Int. J. Forecasting. 12, 465–473 (1996)

    Article  Google Scholar 

  • Čenis, A., Lasiene, G., Pyragas, K.: Estimation of interrelation between chaotic observable. Phys. D. 52, 332–337 (1991)

    Article  MathSciNet  Google Scholar 

  • Clemens, J.C.: Whole Earth telescope observations of the white dwarf star PG 1159-035 (data set E). In: Gerschenfeld, N.A., Weigend, A.S. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past. SFI Studies in the Science of Complexity, Proc. V. XV, pp. 139–150. Addison-Wesley, New York (1993)

    Google Scholar 

  • Eckmann, J.-P., Kamphorst, S.O., Ruelle, D.: Recurrence plots of dynamical systems. Europhys. Lett. 5, 973–977 (1987)

    Article  ADS  Google Scholar 

  • Facchini, A., Kantz, H., Tiezzi, E.: Recurrence plot analysis of nonstationary data: the understanding of curved patterns. Phys. Rev. E. 72, 021915 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  • Fraser, A.M., Swinney, H.L.: Independent coordinates for strange attractors from mutual information. Phys. Rev. A. 33, 1131–1140 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  • Frik, P., Sokolov, D.: Wavelets in astrophysics and geophysics. Computerra, vol. 8. Available at http://offline.computerra.ru/1998/236/1125/ (in Russian) (1998)

  • Gabor, D.: Theory of communication. J. Inst. Elect. Eng. (London). 93, 429–459 (1946)

    Google Scholar 

  • Gribkov, D., Gribkova, V.: Learning dynamics from nonstationary time series: analysis of electroencephalograms. Phys. Rev. E. 61, 6538–6545 (2000)

    Article  ADS  Google Scholar 

  • Groth, A.: Visualization of coupling in time series by order recurrence plots. Phys. Rev. E. 72, 046220 (2005)

    Article  ADS  Google Scholar 

  • Hamming, R.W.: Digital Filters, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ (1983)

    Google Scholar 

  • Herman, S.L.: Delmar’s Standard Textbook of Electricity. Delmar Publishers, San Francisco (2008)

    Google Scholar 

  • Huang, N.E., Shen, Z., Long, S.R.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A. 454, 903–995 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Hubner, U., Weiss, C.-O., Abraham, N.B., Tang, D.: Lorenz-like chaos in \(\mathit{NH}_{3} - \mathit{FIR}\) lasers (data set A). In: Gerschenfeld, N.A., Weigend, A.S. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past. SFI Studies in the Science of Complexity, Proc. V. XV, pp. 73–104. Addison-Wesley, New York (1993)

    Google Scholar 

  • Jenkins, G., Watts, D.: Spectral Analysis and Its Applications. Holden-Day, New York (1968)

    Google Scholar 

  • Judd, K., Mees, A.I. On selecting models for nonlinear time series. Phys. D. 82, 426–444 (1995)

    Article  MATH  Google Scholar 

  • Kalashnikov, S.G.: Electricity. Nauka, Moscow, (in Russian) (1970)

    Google Scholar 

  • Keller, C.F.: Climate, modeling, and predictability. Phys. D. 133, 296–308 (1999)

    Article  MATH  Google Scholar 

  • Kendall, M.G., Stuart, A.: The Advanced Theory of Statistics, vols. 2 and 3. Charles Griffin, London (1979)

    Google Scholar 

  • Kennel, M.B.: Statistical test for dynamical nonstationarity in observed time-series data. Phys. Rev. E. 56, 316–321 (1997)

    Article  ADS  Google Scholar 

  • Koronovskii, A.A., Hramov, A.E.: Continuous Wavelet Analysis in Application to Nonlinear Dynamics Problems. College, Saratov (2003)

    Google Scholar 

  • Koronovskii, N.V., Abramov, V.A.: Earthquakes: causes, consequences, forecast. Soros Educ. J. 12, 71–78, (in Russian) (1998)

    Google Scholar 

  • Kugiumtzis, D., Lingjaerde, O.C., Christophersen, N.: Regularized local linear prediction of chaotic time series. Phys. D. 112, 344–360 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Lachaux, J.P., Rodriguez, E., Le Van Quyen, M., et al.: Studying single-trials of phase synchronous activity in the brain. Int. J. Bif. Chaos. 10, 2429–2455 (2000)

    Google Scholar 

  • Lean, J., Rottman, G., Harder, J., Kopp, G.: Source contributions to new understanding of global change and solar variability. Solar Phys. 230, 27–53 (2005)

    Article  ADS  Google Scholar 

  • Lequarre, J.Y.: Foreign currency dealing: a brief introduction (data set C). In: Gerschenfeld, N.A., Weigend, A.S. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past. SFI Studies in the Science of Complexity, Proc. V. XV, pp. 131–137. Addison-Wesley, New York (1993)

    Google Scholar 

  • Letellier, C., Le Sceller, L., Gouesbet, G., et al.: Recovering deterministic behavior from experimental time series in mixing reactor. AIChE J. 43(9), 2194–2202 (1997)

    Article  Google Scholar 

  • Letellier, C., Macquet, J., Le Sceller, L., et al. On the non-equivalence of observables in phase space reconstructions from recorded time series. J. Phys. A: Math. Gen. 31, 7913–7927 (1998)

    Article  ADS  MATH  Google Scholar 

  • Ljung, L.: System Identification. Theory for the User. Prentice-Hall, New York (1991)

    Google Scholar 

  • Makarenko, N.G.: Embedology and neuro-prediction. Procs. V All-Russian Conf. “Neuroinformatics-2003”. Part 1, pp. 86–148, Moscow, (in Russian) (2003)

    Google Scholar 

  • Maraun, D., Kurths, J.: Cross wavelet analysis: significance testing and pitfalls. Nonlin. Proc. Geophys. 11, 505–514 (2004)

    Article  ADS  Google Scholar 

  • Marwan, N., Kurths, J.: Nonlinear analysis of bivariate data with cross recurrence plots. Phys. Lett. A. 302, 299–307 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Marwan, N., Kurths, J.: Cross recurrence plots and their applications. In: Benton, C.V. (ed.) Mathematical Physics Research at the Cutting Edge, pp. 101–139. Nova Science Publishers, Hauppauge (2004)

    Google Scholar 

  • Marwan, N., Romano, M.C., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  • Marwan, N.: Encounters with Neighbours – Current Developments of Concepts Based on Recurrence Plots and Their Applications. Ph.D. Thesis. University of Potsdam, Potsdam (2003)

    Google Scholar 

  • Misiti, R. et al. Wavelet Toolbox. User Guide for MatLab. The second edition (2000)

    Google Scholar 

  • Monin, A.S., Piterbarg, L.I.: About predictability of weather and climate. In: Kravtsov, Yu.A. (ed.) Limits of Predictability, pp. 12–39. TsentrCom, Moscow, (in Russian) (1997)

    Google Scholar 

  • Mudrov, V.L., Kushko, V.L.: Methods of Measurement Processing. Sov. Radio, Moscow, (in Russian) (1976)

    Google Scholar 

  • Pecora, L.M., Carroll, T.L., Heagy, J.F.: Statistics for mathematical properties of maps between time series embeddings. Phys. Rev. E. 52, 3420–3439 (1995)

    Article  ADS  Google Scholar 

  • Pikovsky, A.S., Rosenblum, M.G., Kurths, J.: Synchronisation. A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  • Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge (1988)

    Google Scholar 

  • Priestley, M.B.: Spectral Analysis and Time Series. Academic, London (1989)

    Google Scholar 

  • Pugachev, V.S.: Theory of Probabilities and Mathematical Statistics. Nauka, Moscow, (in Russian) (1979)

    Google Scholar 

  • Pugachev, V.S.: Probability Theory and Mathematical Statistics for Engineers. Pergamon Press, Oxford (1984)

    Google Scholar 

  • Rabiner, L.R., Gold, B.: Theory and Applications of Digital Signal Processing. Prentice Hall, New York (1975)

    Google Scholar 

  • Rieke, C., Sternickel, K., Andrzejak, R.G., Elger, C.E., David, P., Lehnertz, K.: Measuring nonstationarity by analyzing the loss of recurrence in dynamical systems. Phys. Rev. Lett. 88, 244102 (2002)

    Article  ADS  Google Scholar 

  • Rigney, D.R., Goldberger, A.L., Ocasio, W.C., et al.: Multi-channel physiological data: Description and analysis (data set B). In: Gerschenfeld, N.A., Weigend, A.S. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past. SFI Studies in the Science of Complexity, Proc. V. XV, pp. 105–129. Addison-Wesley, New York (1993)

    Google Scholar 

  • Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., Abarbanel, H.D.I.: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E. 51, 980–994 (1995)

    Article  ADS  Google Scholar 

  • Sadovsky, M.A., Pisarenko, V.F.: About time series forecast. In: Kravtsov, Yu.A. (ed.) Limits of Predictability, pp. 158–169. TsentrCom, Moscow (in Russian) (1997)

    Google Scholar 

  • Sato, M., Hansen, J.E., McCormick, M.P., Pollack, J.B.: Stratospheric aerosol optical depths, 1850–1990. J. Geophys. Res. 98, 22987–22994 (1993)

    Article  ADS  Google Scholar 

  • Schiff, S.J., So, P., Chang, T., Burke, R.E., Sauer, T.: Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Phys. Rev. E. 54, 6708–6724 (1996)

    Article  ADS  Google Scholar 

  • Schreiber, T.: Detecting and analyzing nonstationarity in a time series using nonlinear cross predictions. Phys. Rev. Lett. 78, 843–846 (1997)

    Article  ADS  Google Scholar 

  • Schreiber, T.: Interdisciplinary application of nonlinear time series methods. Phys. Rep. 308, 3082–3145 (1999)

    Article  MathSciNet  Google Scholar 

  • Sena, L.A.: Units of Physical Quantities and Their Dimensions. Nauka, Moscow (1977). Translated into English: Mir Publ., Moscow (1982)

    Google Scholar 

  • Soofi, A.S., Cao, L. (eds.): Modeling and Forecasting Financial Data: Techniques of Nonlinear Dynamics. Kluwer, Dordrecht (2002)

    Google Scholar 

  • Timmer, J., Lauk, M., Pfleger, W., Deuschl, G.: Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized elecromyogram. Biol. Cybern. 78, 349–357 (1998)

    MATH  Google Scholar 

  • Torrence, C., Compo, G. A prectical guide to wavelet analysis. Bull. Amer. Meteor. Soc. 79, 61–78 (1998)

    Article  Google Scholar 

  • Trubetskov, D.I.: Oscillations and Waves for Humanitarians. College, Saratov, (in Russian) (1997)

    Google Scholar 

  • von Mises, R.: Mathematical Theory of Probability and Statistics. Academic Press, New York (1964)

    Google Scholar 

  • Yule, G.U.: On a method of investigating periodicities in disturbed series, with special reference to Wolfer’s sunspot numbers. Phil. Trans. R. Soc. London A. 226, 267–298 (1927)

    Article  ADS  MATH  Google Scholar 

  • Zbilut, J.P., Giuliani, A., Webber, C.L.: Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification. Phys. Lett. A. 246, 122–128 (1998)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Saratov State University, Astrakhanskaya Street 83, 410012, Saratov, Russia

    Prof. Boris P. Bezruchko

  2. Russian Academy of Science, V.A. Kotel’nikov Institute of RadioEngineering and Electronics, Saratov Branch, Zelyonaya Str. 38, 410019, Saratov, Russia

    Dr. Dmitry A. Smirnov

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  1. Prof. Boris P. Bezruchko
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Correspondence to Boris P. Bezruchko .

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Bezruchko, B.P., Smirnov, D.A. (2010). Data Series as a Source for Modelling. In: Extracting Knowledge From Time Series. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12601-7_6

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