this is for holding javascript data
Gordon Richards edited untitled.tex
over 7 years ago
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%define stationary
%are lightcurves stationary?
%**mention light curves as the time-series we're talking about
Analysis of astronomical time-dependent data sets requires methods of quantifying and parameterizing the properties of the observed process in order to learn about the underlying physical processes driving them. The most common method of parameterization of light curve variability currently is to compute the structure function. The structure function is useful because it allows us to relate the variation in brightness to the period of time over which we observe the change. The structure function
is can be characterized
by in a number of ways, the simplest of which is with a power law with a slope and y-intercept as free
parameters. parameters [GTR: Add citation, e.g. Schmidt et al. 2010]. While a useful tool,
it the structure function lacks the sophistication required to probe the complex behavior of
AGN which AGN.
%which require far more parameters to effectively model due to their complicated structure.
Instead, we look to other tools commonly used in time-series analysis.
Most astronomical time-series obey the properties of a stationary process. %why?
A process $X_t, t \in \Z$ is said to be a {\em stationary process} if (i) $X_t$ has finite variance for all $t$, (ii) the expectation value of $X_t$ is constant for all $t$, and (iii) the autocovariance function, $\gamma_{X}(r,s) = \gamma_{X}(r+t, s+t)$, for all $r,s,t \in \Z$.