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Simulation of Markov chains by TRANSFORM

TRANSFORM <data> BY #MARKOV(P)
                    makes random values according to a Markov chain.
                    Each observation (variables X1,X2,...,Xm)
                    will contain one realization of the chain
                    and starts from state given by START=i (i=1,2,...).
                    Default is START=1.
                    The transition probabilities are given as
                    a square matrix P.

TRANSFORM <data> BY #MARKOV(P,<var>,<n>)
                    works as the previous operation but only
                    saves the state of the chain in <var> 
                    after <n> steps.

Also Markov chains of degrees 2,3,...,8 can be simulated by the two
TRANSFORM operations above. Then the P matrix has dimensions m^k,m,
k=2,3,...,8. The start state is in these cases always the first one.
See an example on the next page!

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Example: Simulation of a 3-state Markov chain of degree 2:
MATRIX P93
///    A   B   C
AA     0.6 0.4 0
AB     0   1   0
AC     0.2 0.2 0.6
BA     0.6 0.2 0.2
BB     0.2 0.2 0.6
BC     0.2 0.2 0.6
CA     1   0   0
CB     0   0   1
CC     0   0   1     / This is a final state!

MAT SAVE P93
FILE MAKE TEST,30,1000,L,S        / Space for 1000 chains of length 30
TRANSFORM TEST BY #MARKOV(P93)    / Generating the chains RND=1111
FILE LOAD -TEST / DELIMITER=NULL  / Loading the chains (3 first shown)
 ABBCAABBAABBAABBAAAABBBCCCCCCC
 AAAABBBAAAABBACCCCCCCCCCCCCCCC
 BBABBAABBAABBCBCBCBCCCCCCCCCCC

  M = More information on Markov chains 
  V = More information on transformations