Gordon Richards edited untitled.tex  over 7 years ago

Commit id: 7eb69230cfdc5bc19434a64a0c29247ed560a7bf

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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 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{\em  stationaryprocess}  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 $r,s,t \in \Z$. %What does this do for us? What are some useful properties relating to ARMA models?  % Can redefine the Autocovariance function (talk about relation to structure function earlier, why it's important to what we want to know)