## LINEAR AND NON-LINEAR TIME SERIES ANALYSIS OF CYG X-1

**J. Timmer,
I. Wardinski, H. Voss, U. Schwarz,
G. Hasinger,
Tomaso Belloni
(EXSAS),
Michael van der Klis, J. Kurths **
PRE 61 (2) 1 February 2000,
Preprint

We analyze the variability in the X-ray lightcurves of the black hole
candidate Cygnus X-1 by linear and nonlinear time series
analysis methods.
While a linear model describes the over-all
second order properties of the observed data well,
surrogate data analysis reveals a significant
deviation from linearity. We discuss the relation between
shot noise models usually applied to analyze these data
and linear stochastic autoregressive models.
We debate statistical and interpretational issues of surrogate data
testing for the present context.
Finally, we suggest a combination of tools from linear and
nonlinear time series analysis methods as a procedure to test
the predictions of astrophysical models on observed data.

*Q(m)* statistics and twice the standard error
calculated from the 32 segments of length 20000 of the second
time series based on the estimated denoised data by the Kalman filter.