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Suppose I have a standard state-space model. The sample is, say, 1990-2015, quarterly data. I assume that in period 1990-2000 there were two sources of noise in the measurement equation, while in 2001-2015 there remained only one noise. I know the date when this "structural break" happened.

What Kalman-like model is the best fit for such situation? Can "Two noises then one noise" be indeed modelled as two separate, identified shocks? Or, may be, it is better to model only one measurement noise but with time-varying sigma?

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  • $\begingroup$ What are you trying to achieve? A state-space formulation brings substantial overheads wrt a GLM or traditional time series model. $\endgroup$ – IcannotFixThis Jan 28 '16 at 7:53
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A straight forward Kalman Filter can handle this right out of the box. The 1D model you describe is the univariate model and your implementation of the Kalman Filter would merely keep the time-stamp ticking up as you filter the time-series, then after you required period, you can increase your measurement noise to what ever value you desire by amending the state-space model.

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