Does this type of process have a name?

[euroazn]

E(X_n+1+i)=Ʃⁿ⁺ⁱ_j=i+1 c_j-iX_j, where
Ʃⁿ_j=1 c_j = 1.
n is a fixed constant here, c is a fixed set of n coefficients.

Can anyone tell me anything about such a process?

 

[mathman]

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

 

[euroazn]

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

 

[Stephen Tashi]

E(X_n+1+i)=Ʃⁿ⁺ⁱ_j=i+1 c_j-iX_j, where
Ʃⁿ_j=1 c_j = 1.
n is a fixed constant here, c is a fixed set of n coefficients.

Can anyone tell me anything about such a process?

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.

 

[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.

 

[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.

 

[euroazn]

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