## 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-]neustroev.net

### 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.

### Literature:

- 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

### Schedule:

**Lecture 1: September 7:**Introduction (Time Series, Light Curves, Time)

PDF**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.

PDF**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.

PDF**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.

PDF**Lecture 13: October 12:**Time Series Analysis in the Time Domain. Cross-Correlation. Autocorrelation. O-C Diagram.

PDF