The final exam will be held on Tuesday, November 3, 2020, at 11.00 in Zoom.

767301A / 767601S

Time Series Analysis in Astronomy


an intermediate & advanced course (5 credits)

at the Space Physics and Astronomy research unit, University of Oulu

The course period: September 7 – October 14, 2020

Lectures, exercise and practical sessions take place in the computer class YL124,
see Peppi for detail.

The course is lectured in English

Teacher: Vitaly Neustroev, MA 302, vitaly[-at-]



Course content:

  • Time Series Analysis: Methods for evenly sampled data
  • Time Series Analysis: Methods for unevenly sampled data
  • Timing methods in Optical and X-ray Astronomy
  • Timing features in Optical and X-ray Astronomy

Theoretical and practical considerations will be supplemented with the home exercises which constitute the important part of the course.



  • Fourier Analysis of Time Series: An Introduction (2nd edition – 2000) – P. Bloomfield: ISBN: 978-0-471-88948-9
  • Asteroseismology (2010) – C. Aerts, J. Christensen-Dalsgaard, D. W. Kurtz: ISBN: 978-1-4020-5178-4
  • Fourier techniques in X-ray timing (1988) – M. van der Klis: can be downloaded from here
  • Fourier Analysis with Unequally-Spaced Data (1975) – T. J. Deeming: can be downloaded from here
  • Astronomical Time Series Analysis: Lecture Notes – Jaan Pelt: can be downloaded from here



  • Lecture 1: September 7: Introduction (Time Series, Light Curves, Time)
  • Lecture 2: September 8: Introduction (Frequency, Phase, Ephemeris, Simplest methods of Time Series Analysis).
    PDF * Light Curve
  • Lecture 3: September 10: Harmonic Analysis. Fourier transform.
  • Lecture 4: September 14: Continuous and Discrete Fourier transforms, Power Density Spectrum.
    PDF * Program set N1 * Light Curve (sin)
  • Lecture 5 and Exercise session: September 15: Discrete FT of a sinusoid.
  • Lecture 6: September 17: Power Density Spectrum. Leahy normallization.
    PDF * Poisson data * Light Curve (eclipses)
  • Lecture 7: September 21: Statistics of Power Spectra. Useful tips.
    PDF * Viewer * TimeRebin * Conf. level data * Simulated data
  • Lecture 8 and Exercise session: September 22:
    Real Data 1
  • Exercise session at home: September 23: Analysis of Real Data
  • Lecture 9: September 28: Spectral Analysis with Unevenly-Spaced Data. Discrete Fourier Transform.
    PDF * Paper (Deeming) * Test Data
  • Lecture 10: September 29: Spectral Analysis with Unevenly-Spaced Data. DFT (cont.).
    PDF (the same file)
  • Lecture 11: October 1: Spectral Analysis with Unevenly-Spaced Data (cont.): Lomb-Scargle periodogram. Combined analysis of power spectra.
    PDF * Paper (Sturrock) * Lomb-Scargle Win * Lomb-Scargle Src
  • Exercise session at home: October 5.
    Real Data 2
  • Lecture 12: October 6: Spectral Analysis with Unevenly-Spaced Data (cont.): Dealing with Aliases. CLEAN algorithm. Non-parametric Frequency Analysis Methods. Comparison of PDM and the LS method.
  • Lecture 13: October 12: Time Series Analysis in the Time Domain. Cross-Correlation. Autocorrelation. O-C Diagram.