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rec11 - MIT OpenCourseWare http/ocw.mit.edu 14.384 Time...

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MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Filtering Kalman filtering is a fancy name for a simple idea. Many people think that Kalman filtering is difficult or complicated because they think of it in terms of an updating algorithm with many steps. In fact, to understand Kalman filtering, it’s best to forget the algorithm and just remember what it’s for. Knowing what Kalman filtering is for, you should be able to derive the entire algorithm in an hour or so. The purpose of Kalman filtering is to compute the likelihood of a state-space model. Suppose we have some model with parameters θ , and we want to compute the likelihood of a sequence, { y t } . Just as when we derived the likelihood for a VAR, we can break the joint likelihood into a product of marginal likelihoods: f ( y 1 , ..., y T ; θ ) = f ( y T | y T 1 , ..., y 1 ; θ ) f ( y T 1 | y T 2 , ..., y 1 ; θ ) ...f ( y 1 ; θ ) T = f ( y t | y t 1 , ..., y 1 ; θ ) t =1 For a
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