It should be pointed out that theorem 2 simply states sufficient conditions, so the BIC, while not satisfying the conditions of the theorem, nevertheless might provide efficient forecasts.

That is, X* = [Rf(Rf-l)-1(var(S ^QX-jQF^j))-1]1^2 (this uses var(e-t) = l), where R? is i.i.d. U(0.1,0.8).
The list used here consists of the leading indicators used to produce the XRI and the XRI-2, which are released monthly at the web site http: //www. nber. org. Additional documentation is available at that site.

Most modern specifications of the Phillips curve treat prices as 1(2) (cf. Gordon [1982, 1997]), but in (5.4), prices are treated as 1(1). An 1(2) specification is achieved in (5.4) by imposing E j =oTj = 1- Forecasts were also computed for this specification. The simulated real time forecasts for the 1(2) specification were slightly worse than those for the 1(1) specification, so only results for the better performing 1(1) specification are reported below.

The contributions to the trace-R by the first six factors are, respectively: 0.156, 0.115, 0.077, 0.046, 0.042, and 0.035, for a total of 0.471.

Appendix A: Proofs of Theorems

The proof of theorem 1 makes use of the following lemma.
Lemma AL Under conditions R, P and M, payday loan online