# Showing that a source is not Markov

If I have some source sending codewords and I take a large sample of codewords in order to construct an empirical distribution of the codewords sent. Using this empirical distribution, what methods can I use to demonstrate/prove (statistically) that the source is not a Markov source?

• Please say more about the domain from which codewords are chosen. Is it continuous ($\mathbb{R}^n$)? Categorical (e.g., $\{0,1\}^n$)? What do you mean by Markov source? Do you mean that the sequence of numbers/bits in the codeword are generated from a Markov model, and each codeword is sampled iid from this same process? Or that the sequence of codewords are generated from a Markov model? – D.W. Apr 29 at 15:12
• The domain is categorical and the sequence of messages are transmitted in a way such that is independent of what previous messages have been sent. So, for instance each message is independent of the message sent before it – KingJ Apr 29 at 23:21
• Can you edit the question accordingly? Thank you! – D.W. Apr 30 at 14:34