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  \section{The Kalman Filter}  Testing a stochastic model for accuracy requires a method of recreating our observed data from our chosen parameters. Since the CARMA model is stochastic, unguided attempts to model our light curve could have an infinite number of different results. We require a method of simulation that takes into account the value of the light curve at each observation, make a prediction of what the next observation will be, compare the observation and the prediction, and finally correct itself for the next step like in a Markov-chain. To do this, we implement a Kalman filter.   To be able to make predictions about the future state of our light curve given it's current state and a specific CARMA model, we need to break down our observations into {\em state space.} (Define better) State space is simply an estimation of the true value of the light-curve at some point in time. By representing our light curve in state space, we can apply a simple transformation to predict the next step in state space. Let $X_{i}$ be the state space vector of our light curve at some observation $i$. We can predict the next observation by  $$X_{i+1} = F_{i}X_{i}+V_{i+1}$$  Where $F_{i}$ is called the {\em transformation matrix} at that observation determined by our CARMA model, and $V_{i}$ is a vector of zero mean Gaussian distributed random variables following a set of covariance matricies, $Q_{i}$, determined by our CARMA model, representing the intrinsic system error.  Observations of a system are generally made by observing some distortion of the system with some observation error. We can transform our state space representation into our observed variables, $Y_{i}$ by the {\em observation equation}.  $$Y{i} = G_{i}X_{i}+W_{i}$$    Where $G_{i}$ is the {\em observation matrix} which in our case will simply represent whether or not the value of the light curve was observed, and $W_{i}$ is a random zero mean vector following a set of known covariance matricies, $R_{i}$, representing the observation error.  AGN light curves only give us a picture of the effects that the underlying physical processes have on the AGN itself, but they don't directly tell us what those physical processes are or how they evolve. Futher more, observation error makes it even more difficult to determine their structure. To understand these processes, we need a method of inspecting the state of the system based on our external observations that can also take into account our observation error. The Kalman filter is a digital filter that attempts to reduce observation error and intrinsic system noise by making predictions about future values of the time-series based on an assumed model using Markov chains. Using a Kalman filter together with our CARMA model, we can accurately model theses underlying physical processes and begin analyzing the true structure of the driving system. In order to effectively use a Kalman filter, we must transform our observations, $y(t)$, into state space, $x(t)$.  $$ y(t) = b x(t) + \epsilon(t)$$ 
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The Kalman filter can be used to estimate the likelihood of a proposed CARMA model by calculating the residuals of the CARMA model with the input time-series.  %need more research on kfilter  Two factors contribute to the need for the Kalman filter. The intrinsic system error in the next step of the process (since Kfilter is markov) and the observation noise.  \section{Fitting CARMA Models}  \subsection{CARMA\_Pack}