Abstract
The statistical treatment of time-series data has a long history of theoretical development, continuing to the present. A number of modern texts are available on the topic (e.g., Cox and Lewis, 1966; Hannan, 1970; Jenkins and Watts, 1969; Kendall, 1973; Koopmans, 1974; Parzen, 1967; Rosenblatt, 1963), and no attempt will be made here to summarize such general treatments. Instead, the approach here is nonmathematical and pragmatic, with emphasis confined to those techniques and issues of interpretation that have proved to be important for research on biological rhythms whose adaptive significance involves the need for an organism to maintain an appropriate phase relationship with a regularly cyclic environment. The physiological process by which a majority of animals accomplish this objective is an endogenous, entrainable rhythm, usually self-sustaining, in which a single frequency or an extremely narrow range of frequencies dominates the animal’s entire physiology and behavior. In such a self-sustaining rhythm, phase is conserved for long intervals, if not indefinitely. These characteristics of biological rhythms create a very special and limited class of problems in data analysis, for which the appropriate and useful techniques are often quite different from those designed for time-series data from other sources.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bingham, C., Godfrey, M.D., and Tukey, J. W. Modern techniques of power spectrum estimation. Institute of Electrical and Electronics Engineers: Transactions on Audio- and Electroacoustics 1967, Au 15, 56–66.
Binkley, S. Computer methods of analysis for biorhythm data. In P. J. DeCoursey (Ed.), Biological Rhythms in the Marine Environment. Columbia: University of South Carolina Press, 1976.
Binkley, S., Adler, K., and Taylor, P. H. Two methods for using period length to study rhythmic phenomena. Journal of Comparative Physiology, 1973, 83, 63–71.
Blume, J. Das Auffinden und der mathematische Nachweis der Existenz von Perioden in komplizierten Kurvenschreiben. Kreislaufforschung, 1955, 44, 461–740.
Cox, D. R., and Lewis, P. A. W. The Statistical Analysis of Series of Events. London: Methuen Co., 1966.
De Prins, J., and Cornélissen, C. Numerical signal averaging. Journal of Interdisciplinary Cycle Research, 1975, 6, 95–102.
Enright, J. T. The tidal rhythm of activity of a sand-beach amphipod. Zeitschrift für vergleichende Physiologie, 1963, 46, 276–313.
Enright, J. T. Accurate geophysical rhythms and frequency analysis. In J. Aschoff (Ed.), Circadian Clocks. Amsterdam: North-Holland, 1965a.
Enright, J. T. The search for rhythmicity in biological time-series. Journal of Theoretical Biology, 1965b, 8, 426–468.
Enright, J. T. Influences of seasonal factors on the activity onset of the house finch. Ecology, 1966, 47, 662–666.
Halberg, F. Organisms as circadian systems: Temporal analysis of their physiologic and pathologic responses, including injury and death. In Medical Aspects of Stress in the Military Climate. Washington, D.C.: Walter Reed Army Institute for Research, 1964.
Halberg, F., Tong, Y. L., and Johnson, E. A. Circadian system phase—An aspect of temporal morphology; procedures and illustrative examples. In H. von Mayersbach (Ed.), The Cellular Aspects of Biorhythms. Berlin: Springer, 1967.
Hannan, E. J. Multiple Time Series. New York: Wiley, 1970.
Jenkins, G. M., and Watts, D. G. Spectral Analysis and Its Applications. San Francisco: Holden-Day, 1969.
Kendall, M. G. Time Series. London: Griffin, 1973.
Koopmans, L. H. The Spectral Analysis of Time Series. New York: Academic, 1974.
Lamprecht, G., and Weber, F. Eine neue Methode zur Bestimmung von Periodenlängen rhythmisch ablaufender physiologischer Prozesse. Pflügers Archiv. European Journal of Physiology, 1970, 315, 262–272.
Lamprecht, G., and Weber, F. Eine neue Methode zur Bestimmung von Periodenlängen II. Das Verfahren der schrittweisen Elimination. Pflügers Archiv. European Journal of Physiology, 1972, 336, 60–71.
Martin, W., and Brinkmann, K. A comparison of the numerical signal averaging of de Prins and Cornélissen and Blume’s Pergressive [sic] Fourier Analysis. Journal of Interdisciplinary Cycle Research, 1977, 8, 409–415.
Parzen, E. Time Series Analysis Papers. San Francisco: Holden Day, 1967.
Pittendrigh, C. S., and Daan, S. A functional analysis of Orcadian pacemakers in nocturnal rodents. I. The stability and lability of spontaneous frequency. Journal of Comparative Physiology, 1976, 106, 223–252.
Rawson, K. S., and DeCoursey, P. J. A comparison of the rhythms of mice and crabs from intertidal and terrestrial habitats. In P. J. DeCoursey (Ed.), Biological Rhythms in the Marine Environment. Columbia: University of South Carolina Press, 1976.
Rosenblatt, M. Time Series Analysis. New York: Wiley, 1963.
Schuster, A. On the investigation of hidden periodicities with application to a supposed 26-day period of meteorological phenomena. Terrestrial Magnetism, 1898, 3, 13–41.
Winfree, A. An integrated view of the resetting of a circadian clock. Journal of Theoretical Biology, 1970, 28, 327–374.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Plenum Press, New York
About this chapter
Cite this chapter
Enright, J.T. (1981). Data Analysis. In: Aschoff, J. (eds) Biological Rhythms. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6552-9_3
Download citation
DOI: https://doi.org/10.1007/978-1-4615-6552-9_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-6554-3
Online ISBN: 978-1-4615-6552-9
eBook Packages: Springer Book Archive