## Question on forecast combinations

Hi All,

Say I have a variable Z that I believe can modelled/forecasted via two different thematic models in the standard regression form:

E1[Z(t+1)] = a1 + b1*X1(t) + c1*Y1(t) + e1(t+1)

E2[Z(t+1)] = a2 + b2*X2(t) + c2*Y2(t) + e2(t+1)

where:
(1) E1[] and E2[] represent the expected values of Z via models 1 and 2 respectively.
(2) a1, a2 are constants
(3) b1, b2, c1, c2 are the regressors
(4) e1, e2 are random error terms
(5) X1, X2, Y1, Y2 are explanatory variables

Accordingly, while there may be some correlation between the variables within each model (e.g. X1 and Y1), it is assumed that there are no correlations between the variables of the different models (e.g. X1 and X2). For example, model 1 is a stock return predictor based on company fundamentals, while model 2 is a stock return predictor based on technical analysis.

The question is: will it be better to combine the forecasts by taking the average of the two model forecasts above, or will it be better to convert each model to become a single variable model and then taking the average forecasts of all four regressions (see below)?

E1[Z(t+1)] = a1 + b1*X1(t) + e1(t+1)
E2[Z(t+1)] = a2 + b2*Y1(t) + e2(t+1)
E3[Z(t+1)] = a3 + b3*X2(t) + e3(t+1)
E4[Z(t+1)] = a4 + b4*Y2(t) + e4(t+1)

I hope my question makes sense and would greatly appreciate any guidance. Thanks in advance.

Best,
NZ