  Conditionally Markov (CM) sequences are powerful mathematical tools for
modeling random phenomena. There are several classes of CM sequences one of
which is the reciprocal sequence. Reciprocal sequences have been widely used in
many areas including image processing, intelligent systems, and acausal
systems. To use them in application, we need not only their applicable dynamic
models, but also some general approaches to designing parameters of dynamic
models. Dynamic models governing two important classes of nonsingular Gaussian
(NG) CM sequences (called $CM_L$ and $CM_F$ models), and a dynamic model
governing the NG reciprocal sequence (called reciprocal $CM_L$ model) were
presented in our previous work. In this paper, these models are studied in more
detail and general approaches are presented for their parameter design. It is
shown that every reciprocal $CM_L$ model can be induced by a Markov model and
parameters of the reciprocal $CM_L$ model can be obtained from those of the
Markov model. Also, it is shown how NG CM sequences can be represented in terms
of an NG Markov sequence and an independent NG vector. This representation
provides a general approach for parameter design of $CM_L$ and $CM_F$ models.
In addition, it leads to a better understanding of CM sequences, including the
reciprocal sequence.
