SOLUTION: Let X and Y be Markov chains on the set;Z of integers. Is the sequence Zn = Xn + Yn necessarily a Markov chain?

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Question 1113790: Let X and Y be Markov chains on the set;Z of integers. Is the sequence Zn = Xn + Yn necessarily a Markov chain?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
No
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if you know Z(n-1) = X(n-1) + Y(n-1), there is no way you can know X(n-1) and Y(n-1) - this means you can not find the distribution of X(n) + Y(n) from the knowledge of X(n-1) + Y(n-1)
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