  Conditionally Markov (CM) sequences are powerful mathematical tools for
modeling problems. One class of CM sequences is the reciprocal sequence. In
application, we need not only CM dynamic models, but also know how to design
model parameters. Models of two important classes of nonsingular Gaussian (NG)
CM sequences, called $CM_L$ and $CM_F$ models, and a model of the NG reciprocal
sequence, called reciprocal $CM_L$ model, were presented in our previous works
and their applications were discussed. In this paper, these models are studied
in more detail, in particular their parameter design. It is shown that every
reciprocal $CM_L$ model can be induced by a Markov model. Then, parameters of
each reciprocal $CM_L$ model can be obtained from those of the Markov model.
Also, it is shown that a NG $CM_L$ ($CM_F$) sequence can be represented by a
sum of a NG Markov sequence and an uncorrelated NG vector. This (necessary and
sufficient) representation provides a basis for designing parameters of a
$CM_L$ ($CM_F$) model. From the CM viewpoint, a representation is also obtained
for NG reciprocal sequences. This representation is simple and reveals an
important property of reciprocal sequences. As a result, the significance of
studying reciprocal sequences from the CM viewpoint is demonstrated. A full
spectrum of dynamic models from a $CM_L$ model to a reciprocal $CM_L$ model is
also presented. Some examples are presented for illustration.
