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Gordon Richards edited untitled.tex
over 7 years ago
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%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.
[GTR: Why is the next paragraph about stationary processes? Sort of odd to segue from a sentence talking about "tools" to
stationary.] stationary. Maybe put the "There exist..." paragraph here instead? And insert the stationary and white noise text as needed (e.g., after the first sentence)?]
Most astronomical time-series obey the properties of a stationary process. %why?
At the most basic level a stationary light curve would be one that has the same mean and variance regardless of where the light curve is sampled. In more detail, a process $X_t, t \in \Z$ is said to be a stationary 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 $r,s,t \in \Z$.