## Institut für Astronomie und Astrophysik## Abteilung AstronomieSand 1, D-72076 Tübingen, Germany |

This is the homepage of the time series analysis group at the Institute for Astronomy and Astrophysics, Sect. Astronomy, in Tübingen (Germany).

We are dealing with problems of the deterministic (periodic) and non-deterministic behavior of astronomical time series measured by X-ray satellites. The object of our work is to develop tools both for analysing and simulating time series in order to improve the understanding of the time dependent processes taking place in the objects observed by satellites (EXOSAT, Ginga, ROSAT, XTE, ASCA).

One of the most fascinating time series is the sunspot number, which exhibits the well know 11y period and which additionally shows irregular behaviour on timescales from days to decades. The number of sunspots reaches a maximum about every 11 years, but successive maxima have spots with reversed magnetic polarity. Thus the whole cycle is 22 years long. At the Earth's surface, magnetometers measure the geomagnetic field magnitude and direction. The figure below (left) shows the AA Yearly Index, a way of quantifying the magnetic disturbances, over the last 120 years superimposed to the sunspot number.

At first glance, observations carried out over time periods of weeks/months suggest that the latter two phenomena are stochastic in nature, but observations over time periods of decades reveal an intriguing cyclic pattern of gradual increase and decrease in the average number of sunspots visible on the solar disk. This was first noted in 1843 by H. Schwabe, an amateur solar astronomer, and provided the first hint of the existence of the sunspot cycle, whose period Schwabe estimated to be about 10 years. Further work revealed that the length of successive sunspot cycles is not strictly constant but varies from 9 to 11.5 years, with an average cycle period of about 10.8 years. The plot shown above (right) is a historical reconstruction of yearly-averaged sunspot group counts (yellow curve), extending all the way back to the first telescopic sunspot observations in the early seventeenth century. The purple curve is the Zürich normalized sunspot number. Note how the amplitude of the cycle, or the peak average number of sunspots seen in a given year, varies from one cycle to the next. Note also how cycles are asymmetric, in that the rise from sunspot minimum to maximum occurs more rapidly than the subsequent fall from sunspot maximum to minimum. Another striking feature on this plot is the dramatically reduced number of sunspots observed in the time period spanning the years 1645-1715. This was first noticed by G. Spörer, and investigated more systematically by E.W. Maunder. This time period is now usually referred to as the Maunder minimum. Proxies of geomagnetic activity such as aurorae (green crosses) correlate well with the sunspot number, in the sense that lower auroral counts are associated with low amplitude sunspot cycles (e.g., 1940-1960), and high counts with high amplitude cycles (1800-1822).

The daily (yellow), monthly (blue) end monthly smoothed (red) sunspot
numbers are plotted for the last cycle, together with the 12 months ahead
predictions (red dots) and the uncertainty interval (green).

The first application of stochastic autoregressive process modelling was performed by Yule (1927) on the yearly sunspot number as introduced in 1848 by the Swiss astronomer Johann Rudolph Wolf. In addition to the well known periodic behaviour, such a stochastic model reveals the existence of an irregular component which can be described by an autoregressive process using a damped oscillator (period=10.91y, tau=34.56y) and a pure relaxator (tau=10.11y), which explains the observed maxima asymmetry in the sunspot cycles.

Some of the points listed below are still under construction, but you will already find some real data.

- Here you find some selected EXOSAT-ME time
series from Active Galactic Nuclei.

The README-File contains more detailed information on the data available. - The following link is a compilation of 500 time series from agriculture, physics to tree-rings: Time Series Data Library
- The FDM Freiburger Zentrum für Datenanalyse und Modellbildung in Freiburg (Germany) has a project group for Characterization und Modelling of Time Series. If you are interested in more details on this subject just contact Dr. Jens Timmer from the FDM in Freiburg (Germany).

In a collaboration with the Freiburger Zentrum für Datenanalyse und Modellbildung we have already developed some tools to simulate and to analyse continous time series.

- Computing a periodogram with fast fourier techniques using the IDL library.
- Estimation of power law noise parameters in the frequency state.
- On generating power law noise.
- Information on the method used.
- IDL algorithm.

- Autoregressive models in time series analysis.
- Simulate AR(q) time series.
- Estimation of AR(q) parameters.

- State space modelling using the EM-algorithm.
- NETLIB, a repository of mathematical software, data and documents.

Furthermore we have already published some of our results concerning time series analysis tools.

- On generating power law
noise

Timmer J., König M., 1995, A&A, 300, 707-710 - Analyzing X-ray variability
by Linear State Space Models

König M., Timmer J., 1997, A&A Suppl.Ser., 124 (3), 589 - The Seyfert Galaxy NGC 6814
- a highly variable X-ray soure

König M., Friedrich S., Staubert R., Timmer J., 1997, A&A, 322, 747-750 - Analyzing X-ray variability by Linear
State Space Models
*(96k gzip'ed Postscript including figures)*

König M., Timmer J., 1996, Astron.Ges. Abstract Series - A new period for the
magnetic white dwarf KPD0253+5052

Friedrich S., König M., Schweizer W., 1997, A&A, 326, 218-220 - Analyzing X-ray variability
by State Space Models - Application to an EXOSAT AGN sample

König M., Timmer J., Staubert R. 1997, D.Maoz et al (eds.), Astronomical Time Series, 265-268, 1997 Kluwer Academic Publishers - Analyzing short-term X-ray
variability of Cygnus X-1 - Application of Linear State Space
Models

Pottschmidt K., König M. 1997, D.Maoz et al (eds.), Astronomical Time Series, 187-190, 1997 Kluwer Academic Publishers - Time Series Analysis of an EXOSAT AGN sample

König M., Wilms J., Staubert R., 1997, A&A, in preparation - Analyzing optical AGN lightcurves by Linear State Space Models

König M., Timmer J., 1997, A&A, in preparation - On the inclination and
binarity of the pulsating pre-white dwarf PG2131+066

Paunzen E., König M., Dreizler S., 1998, A&A, 331, 162 - Search for Variables in the TYCHO Data Stream

Friedrich S., König M., Wicenec A., TYCHO conference proceedings, Venice 1997 - Correlation between
variability timescale and X-ray spectral index in AGN

König M., Staubert R., Wilms J, 1997, A&A, 326, L25 - A new bright X-ray
galaxy

König M., Geckeler R., Staubert R., 1997, A&A, 329, 68 - On a possible 13.81d period
of the X-ray binary 4U1700-377

König M., Maisack M., 1997, A&A, 327, L33 - The irregular temporal behaviour of the variable star R Scuti

König M., Paunzen E., Timmer J., 1997, MNRAS, accepted - Linear State Space Modeling of
Gamma-Ray Burst Lightcurves
*(67k gzip'ed Postscript including figures)*

Band D., König M., Chernenko A., 1997, GRB Symposium, Huntsville, USA - Analyzing short-term X-ray
variability of Cygnus X-1 with Linear State Space Models

Pottschmidt K., König M., Wilms J., Staubert R. 1998, A&A, 334, 201 - Zeitvariabilität in
Aktiven Galaxien

Michael König, PhD thesis, 1997, University of Tübingen - Anwendung
Linearer Zustandsraummodelle auf die Kurzzeitvariabilität des
Schwarzlochkandidaten Cygnus X-1
*(1.056k gzip'ed Postscript including figures)*

Katja Pottschmidt, diploma thesis, 1997, University of Tübingen

Here are some links to get more fancy stuff on data and how to work with.

- Astronomy Software Resources
- The Bureau of Labour Statictics offers an exemplary homepage with a time series database and corresponding analysis methods.
- Find some weather data at the IMK Institut für Meterologie & Klimaforschung
- You can also retrieve some temperature time series of 200 years length measured in american and european cities from the database of the National Climatic Data Center (NCDC)
- Comet Online Page

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Katja Pottschmidt
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Last modified 16 Aug 2005 |