Greetings,
I am an econometrician exploring the use of Bayesian methods to forecast asset returns (e.g., equities, bonds, etc.). My question centers on accounting for the variability of future values of the explanatory variables. For instance, consider the standard linear regression model, y(t) = a + b*x(t) + e(t), t=1,2,..,T. My question concerns the estimation of future unobserbed values y(t), where t=T+1,T+2,....To estimate future values of y(t), the values x(T+1),x(T+2),..., must be specified. In a Bayesian framework, how might this problem be approached? My aim is estimate the posterior density of the forecasted values, recognizing the fact that the x(t) have not yet been observed.
Initially, there seem to be two "obvious" procedures. The first is to specify some "auxilliary" model for the x(t) process itself. The second is to somehow establish some sequence of x(t) values, under the assumption that the x(t) process is governed by some (prior) probability distribution, and then calculate the resulting posterior.
Thanks and Happy New Year,
Mark
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