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Does this type of process have a name?

  1. Apr 3, 2013 #1
    E(Xn+1+i)=Ʃn+ij=i+1 cj-iXj, where
    Ʃnj=1 cj = 1.
    n is a fixed constant here, c is a fixed set of n coefficients.

    Can anyone tell me anything about such a process?
  2. jcsd
  3. Apr 3, 2013 #2


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    It looks like some sort of generalization of a Markov process.
  4. Apr 7, 2013 #3
    Is it markov if we consider states to be vectors of the past n states?
  5. Apr 8, 2013 #4

    Stephen Tashi

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    You haven't defined a stochastic process. I assume the [itex] X_k [/itex] are random variables. The equation you gave only specifies the expected value of [itex] X_k [/itex] in terms of the realizations of some other [itex] X_j [/itex]. It doesn't specify any distribution for [itex] X_k [/itex]. It doesn't specify whether the distribution of [itex] X_k [/itex] is or is-not independent of other random variables that don't appear in the sum.
  6. Apr 8, 2013 #5
    Oh, I am well aware that it doesn't DEFINE a stochastic process, but if it were to satisfy these conditions, do we know anything nifty about the process?

    Edit: The random X's form a time series if that's not clear.
    Last edited: Apr 8, 2013
  7. Apr 8, 2013 #6

    Stephen Tashi

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    You have to say something about the independence (or lack of it) between different [itex] X[/itex]'s before you can determine if the process can be viewed as a Markov process. It is perfectly OK to use a vector of values as a "state" in a Markov process. The "states" can even be vectors of different lengths.

    An "auto-regressive moving average" model might fit your equation. Make the additive noise term have zero mean.
  8. Apr 8, 2013 #7
    Yes, this is perfect. I think ARMA is exactly what I'm looking for. Thanks a bundle!
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