This note provides explanations for an unexpected result, namely, the estimated parameter of the
correlation coefficient of the trend shock and cycle shock in the state–space model is almost always
(positive or negative) unity, even when the true variance of the trend shock is zero. It is shown that the
set of the true parameter values lies on the restriction that requires the variance–covariance matrix of
the errors to be nonsingular, therefore, almost always the likelihood function has its (constrained) global
maximum on the boundary where the correlation coefficient implies perfect correlation