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\subsection{ARMA}  **Talk %**Talk  about using white noise to drive the process There %**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 characterized by a power law with a slope and y-intercept as free parameters. While a useful tool, it lacks the sophistication required to probe the complex behavior of AGN which require far more parameters to effectively model. Fortunately, there  exist a class of finite difference equations used in the analysis of discrete time series known as autoregressive-moving average (ARMA) processes. These processes give us a way of inspecting the behavior of time-series with a simple but thoroughly descriptive  parametric structure. A stationary process $\{X_t\}$ is an ARMA(p,q) process if at every time $t$ $$X_t - \phi_1X_{t-1} - ... - \phi_pX_{t-p} = Z_t + \theta_{t-1} + ... + \theta_qZ_{t-q} $$  where $\{Z_t\}$ is a white noise process with zero mean and variance $\sigma^2$. For any autocovariance function $\gamma(h)$ for which $\lim_{h\to\infty}\gamma(h) = 0$ and any integer $k > 0$, there exists an ARMA(p,q) process with autocovariance function $\gamma_X(h)$ such that $\gamma_X(h) = \gamma(h)$ for all $h \leq k$. This makes These relations make  the ARMA process a very useful tool in the analysis and modeling of many different time-series. (reword %(reword  this blurb, too much directly from the text) Unfortunately, the phenomena we are observing are not discrete processes, so in order to get a proper understanding of the underlying physics, we need a continuous analog to the ARMA process. \!\!BE %\!\!BE  SURE TO CITE BROCKWELL AND DAVIS TIME SERIES THEORY AND METHODS %**Quick intro to ARMA (an maybe a bit of stochastic analysis)  %***Background, current use