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I have a set of ordinal data, generated by a hypothetical turing machine. The data consists of a sequence of symbols such as:

LB1, LB2, UU, UB1 ...

The labels have a natural ordering, and the machine "prints" out the symbols at an irregular pace.

I would like to analyze, for the purposes of determining (with a degree of certainty), given the history of printed symbols:

  1. How long before the next symbol is printed by the machine.
  2. The most likely next symbol to be generated by the machine.
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It is not clear from your question what "symbols" and "labels" are. – cyborg Jan 6 '12 at 12:53
I use the two terms interchangeably (I admit that may be confusing). For the sake of keeping with the turing mahine analogy, I will stick to the single term "symbol". The "data" represents the set of all of the symbols printed out by the turing machine. The symbols are strings (words if you like) drawn from a finite vocabulary. One could argue that the series of symbols actually form sentences, and that there could be an "implied grammar" to the series of symbols emitted by the turing machine - but I digress ... – Homunculus Reticulli Jan 6 '12 at 13:06

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(Statistical) language modeling deals with such problems.

From simple to more complex options:

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+1 for suggesting language modelling (I had never even heard of it!). I suspected there was a markov property to the sequences though ... all in all, great links for reading up on this subject. I'll wait and see if there are any more suggestions/answers. – Homunculus Reticulli Jan 6 '12 at 13:40

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