The analysis of some bivariate astronomical time series
Master Thesis
1993
Permanent link to this Item
Authors
Supervisors
Journal Title
Link to Journal
Journal ISSN
Volume Title
Publisher
Publisher
University of Cape Town
Department
Faculty
License
Series
Abstract
In the first part of the thesis, a linear time domain transfer function is fitted to satellite observations of a variable galaxy, NGC5548. The transfer functions relate an input series (ultraviolet continuum flux) to an output series (emission line flux). The methodology for fitting transfer function is briefly described. The autocorrelation structure of the observations of NGC5548 in different electromagnetic spectral bands is investigated, and appropriate univariate autoregressive moving average models given. The results of extensive transfer function fitting using respectively the λ1337 and λ1350 continuum variations as input series, are presented. There is little evidence for a dead time in the response of the emission line variations which are presumed driven by the continuum. Part 2 of the thesis is devoted to the estimation of the lag between two irregularly spaced astronomical time series. Lag estimation methods which have been used in the astronomy literature are reviewed. Some problems are pointed out, particularly the influence of autocorrelation and non-stationarity of the series. If the two series can be modelled as random walks, both these problems can be dealt with efficiently. Maximum likelihood estimation of the random walk and measurement error variances, as well as the lag between the two series, is discussed. Large-sample properties of the estimators are derived. An efficient computational procedure for the likelihood which exploits the sparseness of the covariance matrix, is briefly described. Results are derived for two example data sets: the variations in the two gravitationally lensed images of a quasar, and brightness changes of the active galaxy NGC3783 in two different wavelengths. The thesis is concluded with a brief consideration of other analysis methods which appear interesting.
Description
Bibliography: pages 75-76.
Reference:
Koen, M. 1993. The analysis of some bivariate astronomical time series. University of Cape Town.