# Does this type of process have a name?

1. Apr 3, 2013

### euroazn

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. Apr 3, 2013

### mathman

It looks like some sort of generalization of a Markov process.

3. Apr 7, 2013

### euroazn

Is it markov if we consider states to be vectors of the past n states?

4. Apr 8, 2013

### Stephen Tashi

You haven't defined a stochastic process. I assume the $X_k$ are random variables. The equation you gave only specifies the expected value of $X_k$ in terms of the realizations of some other $X_j$. It doesn't specify any distribution for $X_k$. It doesn't specify whether the distribution of $X_k$ is or is-not independent of other random variables that don't appear in the sum.

5. Apr 8, 2013

### euroazn

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
6. Apr 8, 2013

### Stephen Tashi

You have to say something about the independence (or lack of it) between different $X$'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.

7. Apr 8, 2013

### euroazn

Yes, this is perfect. I think ARMA is exactly what I'm looking for. Thanks a bundle!