  One of the main problem in prediction theory of stationary processes $X(t)$
is to describe the asymptotic behavior of the best linear mean squared
prediction error in predicting $X(0)$ given $ X(t),$ $-n\le t\le-1$, as $n$
goes to infinity. This behavior depends on the regularity (deterministic or
non-deterministic) of the process $X(t)$. In his seminal paper {\it 'Some
purely deterministic processes' (J. of Math. and Mech.,} {\bf 6}(6), 801-810,
1957), for a specific spectral density that has a very high order contact with
zero M. Rosenblatt showed that the prediction error behaves like a power as
$n\to\f$. In the paper Babayan et al. {\it 'Extensions of Rosenblatt's results
on the asymptotic behavior of the prediction error for deterministic stationary
sequences' (J. Time Ser. Anal.} {\bf 42}, 622-652, 2021), Rosenblatt's result
was extended to the class of spectral densities of the form $f=f_dg$, where
$f_d$ is the spectral density of a deterministic process that has a very high
order contact with zero, while $g$ is a function that can have polynomial type
singularities. In this paper, we describe new extensions of the above quoted
results in the case where the function $g$ can have {\it arbitrary power type
singularities}. Examples illustrate the obtained results.
