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Institut für Astronomie und Astrophysik

Abteilung Astronomie

Sand 1, D-72076 Tübingen, Germany
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Time Series Analysis

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).


The Sunspot Number Time Series

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.

[sunspot number/AA yearly index 1870-1990]

[sunspot group counts/sunspot number 1600-today]

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).

[sunspot number 1986-1998]

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.


Time Series Database

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


Tools

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.


Publications

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


Related Astronomy and Science Links

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


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Katja Pottschmidt | Impressum
Last modified 16 Aug 2005
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