Period Analysis of Astronomical
Time Series:
A Non-Parametric Approach
Elke Kestens, Jef L. Teugels,
Conny Aerts, and Jan Cuypers
Period analysis is nothing more than
searching for periods in a signal. Many techniques exist but we will only
look at methods that can be applied to astronomical time series. The latter
data show a very typical pattern: the measurements of the varying observable
are done with lots of gaps, too large to be treated with existing time
series methods.
Methods that look for periods without
choosing an a priori model are preferable for variable stars. Important
concepts are the phase diagram and the weighted string length statistic.
First, the period that minimizes this statistic has to be found. With this
statistic, test-statistics are defined, taking values between 0 and 1.
The closer to zero, the more significant the period.
Simulations on sine signals show
that minimizing weighted string length statistic performs as good as fitting
a priori known models. The statistic will still be useful when no a priori
model is known, a more realistic assumption when we realise the wide variety
of variable star types. A filtering method for the statistic is developed
and simulated annealing is applied to find the periods with the smallest
teststatistic. The final outcome of this research project between statisticians
and astronomers should be a hypothesis test for the following questions
:
A partial answer to the first question is based on the construction of non parametric confidence intervals using jackknife procedures on the teststatistic.
- Is the star variable, is periodicity present in the signal ?
- How many significant periods are present in the signal ?
- Which model fits the signal ?
ELKE KESTENS
Department: Mathematics
Katholieke Universiteit Leuven
W de Croylaan 52 B
Heverlee, B-3001, Belgium
elke.kestens@ucs.kuleuven.ac.be
On Solar Neutrinos, Sunspots,
and Correlation Statistics
Guenther Walther
A possible time variability of the solar neutrino data has been of lasting interest. Here I will focus on a claimed anticorrelation of the neutrino flux with indicators of the solar cycle, and the accompanying correlation statistics. The main issue will be some problems with these and related statistical procedures that seem not to be well enough appreciated, and some new statistical techniques to circumvent these problems.
GUENTHER WALTHER
Department of Statistics
Stanford University
390 Serra Mall
Stanford, CA 94305, USA
walther@stat.stanford.edu
