Conjecture on eigenvalues of the reduced spectral covariance matrix

Let $\IGamma_{yy}$ and $\bGamma_{yy|x}$ be the matrices arising from the single-regression Granger-causality estimator, and let $\lambda_i$ denote the eigenvalues of $\IGamma_{yy}\bGamma_{yy|x}$, for $i=1,\ldots,pn_y$. The process is assumed to be purely nondeterministic, so these eigenvalues are positive. Eigenvalue conjecture. The eigenvalues satisfy

$$\lambda_i \le 1 \quad\text{for } i=1,\ldots,pn_y.$$

This bound would constrain the shape of the Gamma approximation to the estimator's sampling distribution. The source reports extensive empirical testing but no rigorous proof, so the conjecture remains open.