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Comparatively new to Bayesian econometrics so apologies if this is a silly question.

I am running a time-varying parameter regression where the parameters are estimated as in Primiceri (2005). My model assumes the time varying coefficients follow a random walk.

Say I have a data sample running from t = 0 - n. I fit the model over the full sample and obtain fitted values for the data (denoted *) as;

y*(t) = a(t) + y(t-1)b(t)

As the state equations are random walks, the optimal prediction of a(t+1) and b(t+1) would be a(t) and b(t) respectively.

This being the case, is the forecast of y(t+1) which uses the parameters as estimated at time t out-of-sample? I.e. if I do:

y*(t+1) = a(t) + y(t)b(t)

Is this equivalent to a one-step, out of sample forecast for y(t+1)? Or, in order to compute out of sample forecasts, do i need to loop the model, updating it with new data at every iteration (e.g. first running it over the sample t=1, then t=1-2, then ... then t=1-n).

Thanks a lot for the clarification!

Primiceri, G.E., 2005. Time varying structural vector autoregressions and monetary policy. The Review of Economic Studies, 72(3), pp.821-852.

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