The two information criteria produced by the residual analysis procedure (discussed on page 26 and 72 of the CATS manual) are the Schwarz (SC) and Hannan-Quinn (HQ) criteria as given in eg., Lutkepohl, 1991, p. 132.
SC = ln det(Sigma_hat) + ((ln T)/T)*(number of freely estimated param) HQ = ln det(Sigma_hat) + ((2lnln T)/T)*(number of freely estimated param)
The calculation of freely estimated parameters may seem a little awkward in the manual, so here are a couple of examples: Suppose the model is a standard, stationary VAR with p endogenous series, k lags and no deterministic or exogenous series. Then d0 = p , d1 = p*(k-1), dk = p, r = p, and we get:
SC = ln det(Sigma_hat) + ((ln T)/T)*p^2*k HQ = ln det(Sigma_hat) + ((2lnln T)/T)*p^2*kas usually seen in textbooks. Imposing the cointegration restriction reduces the number of parameters in the model, and the number of estimated parameters is calculated as:
number of paramerers: d0*d1 + d0*r + dk*r - r*r in matrix : Gamma + alpha + beta - normalization of betawhich leads to the formulae in the manual.
A couple of papers have proposed to use the information criteria when testing the cointegration rank and non-nested hypotheses about alpha and beta.
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