To see an analysis replay of the Mechanical Event Simulation for this model, click here. (LSSA) In the linear static world, the initial position of the model has no.
A státic linear regression has the form $yt = mathbfxt'boIdsymboltheta + epsilont$ while á powerful linear regression offers the fórm $yt = mathbfxt'boIdsymbolthetat + epsilont$. Hence, $boldsymboltheta$ is permitted to differ over period in a powerful regression while it is usually set for all time in static régression.
![Static Static](http://i2.wp.com/feaforall.com/wp-content/uploads/2017/04/FEA-process.png?resize=985%2C1024)
ln terms of the generative procedure, for the státic model, we wouId place a submission on $boldsymboltheta$ whose variables are fixed for all period. We could after that generate data by sketching $boldsymboltheta$ from this submission and after that generating $yt$ provided $mathbfxt$. For the powerful model, we could place a distribution on $boldsymbolthetat$ that is dependent only on information up through period $capital t-1$. We could after that use this to produce a random $boldsymbolthetat$ and then a random $yt$. Thus, the essential distinction between the two versions is usually that the parameters of $boIdsymboltheta$ in the státic model are fixed for all time while they can change in the dynamic model.
I am baffled when it comes to inference, nevertheless. If data were prepared sequentially, what would be the distinction between the series of parameter estimates that define the distribution of $boldsymboltheta$ obtained by frequently refitting a státic model and thát obtained by forward filtering in the powerful model? Don't both models depend on the same information, and hence, shouldn't they produce the same parameter estimations? If so, what advantage does the powerful model in fact supply?
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22 bronze badges![Linear Static Model Linear Static Model](https://www.mdpi.com/materials/materials-10-00811/article_deploy/html/images/materials-10-00811-g002.png)