It is well known that the prediction problem for a stationary process can be reduced to that of factorizing a positive-definite matrix function \(S(t)\) as \(S(t)= \chi^+(t)\cdot(\chi^+(t))^*\), \(|t|= 1\), where \(\chi^+\) is an outer analytic matrix function with entries of Hardy class \(H_2\) and \(^*\) denotes the Hermitian conjugate. It is asserted that given positive-definite matrix functions \((S_n)_{n\geq 1}\) and \(S\) such that the logarithms of their determinants are integrable over \(\{t:|t|=1\}\) and \(\|S_n- S\|_{L^1([0, 2\pi))}\to 0\) as \(n\to \infty\) (by which componentwise convergence is meant), we have \(\|\chi^+_n- \chi^+\|_{H_2}\to 0\) if and only if \(\log\det S_n@>\text{weakly}>>\log\det S\), where by weak convergence of a sequence in \(L^1([0, 2\pi))\) there is meant weak convergence of the corresponding sequence of functionals on \(C([0, 2\pi))\). The authors give just hints for a proof.