Time Series Analysis: From Standard to Advanced

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course at ICBM

course at IUB

Keywords:

  • data records, measurements, natural symbol strings
  • stationary vs. non-stationary processes
  • trends, seasonality and residuals
  • filters and autoregressive processes
  • correlations and spectral methods (power spectrum, coherence function)
  • sliding spectra and wavelet based methods
  • attractors: Lyapunov spectra and dimensions
  • attractor reconstruction: embedding techniques and Takens theorem
  • symbolic dynamics, static and dynamic partitions
  • symbol strings and information measures
  • noisy time series: noise reduction and noise vs.~chaos

References:

  1. R. Schlittgen and B. H. J. Streitberg: Zeitreihenanalyse, (Oldenbourg, München, 2001).
  2. M. Priestley: Spectral Analysis and Time Series vols. 1 and 2, (Academic Press, London, 1994).
  3. R.H. Shumway and D.S. Stoffer: Time Series Analysis and Its Applications, Springer Texts in Statistics, (Springer, New York, 2000).
  4. H. Kantz and T. Schreiber: Nonlinear Time Series Analysis, (Cambridge UP, Cambridge, 1997).
  5. R. Hegger, H. Kantz, and T. Schreiber: TISEAN, (web-resources).
  6. H.D.I. Abarbanel: Analysis of Observed Chaotic Data, (Springer, New York, 1996).
  7. A. Galka: Topics in Nonlinear Time Series Analysis - With Implications for EEG Analysis, (World Scientific, Singapore, 2000).

           
Revised 4.14.04