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Time-Series Analysis

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MATLAB® Recipes for Earth Sciences

Abstract

Time-series analysis aims to investigate the temporal behavior of a variable x(t). Examples include the investigation of long-term records of mountain uplift, sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millennium-scale variations in the atmosphere-ocean system, the effect of the El Nino/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1), and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic, or chaotic. Time-series analysis provides various tools with which to detect these temporal patterns. Understanding the underlying processes that produced the observed data allows us to predict future values of the variable.

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Recommended Reading

  • Ansari AR, Bradley RA (1960) Rank-Sum Tests for Dispersion. Annals of Mathematical Statistics, 31:1174–1189. [Open access]

    Google Scholar 

  • Blackman, RB, Tukey, JW (1958) The Measurement of Power Spectra. Dover NY

    Google Scholar 

  • Cooley JW, Tukey JW (1965) An Algorithm for the Machine Calculation of Complex Fourier Series. Mathematics of Computation 19(90):297–301.

    Google Scholar 

  • Donner RV, Heitzig J, Donges JF, Zou Y, Marwan N, Kurths J (2011) The Geometry of Chaotic Dynamics – A Complex Network Perspective. European Physical Journal B, 84:653–672

    Google Scholar 

  • Eckmann JP, Kamphorst SO, Ruelle D (1987) Recurrence Plots of Dynamical Systems. Europhysics Letters 5:973–977

    Google Scholar 

  • Grenander U (1958) Bandwidth and variance in estimation of the spectrum. Journal of the Royal Statistical Society Series B 20:152–157

    Google Scholar 

  • Holschneider M (1995) Wavelets, an Analysis Tool. Oxford University Press, Oxford

    Google Scholar 

  • Kantz H, Schreiber T (1997) Nonlinear Time Series Analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Lau KM, Weng H (1995) Climate Signal Detection Using Wavelet Transform: How to make a Time Series Sing. Bulletin of the American Meteorological Society 76:2391–2402

    Google Scholar 

  • Lepage Y (1971) A combination of Wilcoxon’s and Ansari-Bradley’s statistics. Biometrika 58:213–271

    Google Scholar 

  • Lomb NR (1972) Least-Squared Frequency Analysis of Unequally Spaced Data. Astro-physics and Space Sciences 39:447–462

    Google Scholar 

  • Lorenz EN (1963) Deterministic Nonperiodic Flow. Journal of Atmospheric Sciences 20:130–141

    Google Scholar 

  • Mackenzie D, Daubechies I, Kleppner D, Mallat S, Meyer Y, Ruskai MB, Weiss G (2001) Wavelets: Seeing the Forest and the Trees. Beyond Discovery, National Academy of Sciences, December 2001, available online at http://www.beyonddiscovery.org

  • Mann, HB, Whitney, DR (1947) On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. Annals of Mathematical Statistics 18:50–60

    Google Scholar 

  • Marwan N, Thiel M, Nowaczyk NR (2002) Cross Recurrence Plot Based Synchronization of Time Series. Nonlinear Processes in Geophysics 9(3/4):325–331

    Google Scholar 

  • Marwan N, Trauth MH, Vuille M, Kurths J (2003) Nonlinear Time-Series Analysis on Present-Day and Pleistocene Precipitation Data from the NW Argentine Andes. Climate Dynamics 21:317–332

    Google Scholar 

  • Marwan N, Romano MC, Thiel M, Kurths J (2007) Recurrence Plots for the Analysis of Complex Systems. Physics Reports, 438: 237–329

    Google Scholar 

  • Marwan N (2011) How to avoid potential pitfalls in recurrence plot based data analysis. International Journal of Bifurcation and Chaos 21:1003–1017

    Google Scholar 

  • MathWorks (2014a) Signal Processing Toolbox – User’s Guide. The MathWorks, Inc., Natick, MA

    Google Scholar 

  • MathWorks (2014b) Wavelet Toolbox – User’s Guide. The MathWorks, Inc., Natick, MA

    Google Scholar 

  • Mudelsee M, Stattegger M (1997) Exploring the structure of the mid-Pleistocene revolution with advanced methods of time-series analysis. International Journal of Earth Sciences 86:499–511

    Google Scholar 

  • Mudelsee M (2000) Ramp function regression: A tool for quantifying climate transitions. Computers and Geosciences 26:293–307

    Google Scholar 

  • Muller RA, MacDonald GJ (2000) Ice Ages and Astronomical Causes – Data, Spectral Analysis and Mechanisms. Springer Verlag, Berlin Heidelberg New York

    Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT (2007) Numerical Recipes: The Art of Scientific Computing – Third Edition. Cambridge University Press, Cambridge

    Google Scholar 

  • Romano M, Thiel M, Kurths J, von Bloh W (2004) Multivariate Recurrence Plots. Physics Letters A 330(3–4):214–223

    Google Scholar 

  • Scargle JD (1981) Studies in Astronomical Time Series Analysis. I. Modeling Random Processes in the Time Domain. The Astrophysical Journal Supplement Series 45:1–71

    Google Scholar 

  • Scargle JD (1982) Studies in Astronomical Time Series Analysis. II. Statistical Aspects of Spectral Analysis of Unevenly Spaced Data. The Astrophysical Journal 263:835–853

    Google Scholar 

  • Scargle JD (1989) Studies in Astronomical Time Series Analysis. III. Fourier Transforms, Autocorrelation Functions, and Cross-Correlation Functions of Unevenly Spaced Data. The Astrophysical Journal 343:874–887

    Google Scholar 

  • Schulz M, Stattegger K (1998) SPECTRUM: Spectral Analysis of Unevenly Spaced Paleoclimatic Time Series. Computers & Geosciences 23:929–945

    Google Scholar 

  • Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terrestrial Magmetism and Atmospheric Electricity 3:13–41

    Google Scholar 

  • Takens F (1981) Detecting Strange Attractors in Turbulence. Lecture Notes in Mathematics, 898:366–381

    Google Scholar 

  • Torrence C, Compo GP (1998) A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79:61–78

    Google Scholar 

  • Trulla LL, Giuliani A, Zbilut JP, Webber Jr CL (1996) Recurrence Quantification Analysis of the Logistic Equation with Transients. Physics Letters A 223(4):255–260

    Google Scholar 

  • Turcotte DL (1992) Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge

    Google Scholar 

  • Trauth MH, Bookhagen B, Marwan N, Strecker MR (2003) Multiple Landslide Clusters Record Quaternary Climate Changes in the NW Argentine Andes. Palaeogeography Palaeoclimatology Palaeoecology 194:109–121

    Google Scholar 

  • Trauth MH, Larrasoana JC, Mudelsee M (2009) Trends, rhythms and events in Plio-Pleistocene African climate. Quaternary Science Reviews 28:399–411

    Google Scholar 

  • Weedon G (2003) Time-Series Analysis and Cyclostratigraphy – Examining Stratigraphic Records of Environmental Change. Cambridge University Press, Cambridge

    Google Scholar 

  • Welch PD (1967) The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms. IEEE Trans. Audio Electroacoustics AU-15:70–73

    Google Scholar 

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Correspondence to Martin H. Trauth .

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Trauth, M.H. (2015). Time-Series Analysis. In: MATLAB® Recipes for Earth Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46244-7_5

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