## 765368A / 765668S

# Time Series Analysis in Astronomy

an intermediate & advanced course (6 credits)

at the Astronomy Division, University of Oulu

#### The course period January 25 – March 24, 2016

#### Lectures, and exercise and practical sessions take place on Monday at 12-14 and Thursday at 10-12 in TÄ 219

#### The course is lectured in English

#### Teacher: Vitaly Neustroev, TÄ 218, ph. 5531930, vitaly.neustroev [at] oulu.fi

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: January 25:**Introduction (Time Series, Light Curves, Time, Frequency, Phase, Ephemeris)

PDF * Light Curve**Lecture 2: January 28:**Continuous and Discrete Fourier transforms, Power Density Spectrum.

PDF**Exercise session: February 1:**Programs N1.

**Exercise session: February 4:**

**Lecture 3: February 8:**Power Density Spectrum. Leahy normallization.

PDF * Poisson data * Light Curve (eclipses) * Light Curve (sin)**Lecture 4: February 11:**Statistics of Power Spectra.

PDF * Conf.zip * Viewer * Real Data 1**Lecture 5: February 18:**Statistics of Power Spectra (cont). Useful tips.

PDF**Lecture 6: February 22:**Spectral Analysis with Unevenly-Spaced Data. Discrete Fourier Transform. Lomb-Scargle periodogram.

PDF * Paper (Deeming) * Lomb-Scargle Win * Lomb-Scargle Src * Test Data**Lecture 7: February 29:**Spectral Analysis with Unevenly-Spaced Data. Combined analysis of power spectra. Dealing with Aliases. CLEAN algorithm.

PDF * Paper (Sturrock)**Lecture 8 (self-study): March 3:**Spectral Analysis with Unevenly-Spaced Data. Non-parametric Frequency Analysis Methods.

PDF**Lecture 9: March 14:**Spectral Analysis with Unevenly-Spaced Data. Comparison of PDM and the LS method.

PDF (same file)**Lecture 10: March 17:**Time Series Analysis in the Time Domain. Cross-Correlation. Autocorrelation. O-C Diagram.

PDF**Lecture 11: March 21:**Conclusion.

PDF**Exercise session: March 24:**

Data for practical work.**Exercise session: April 4****Exercise session: April 7****Final exercise session: April 11**