What Is an M-Dependent Stationary Process?

[New_Galatea]

[SOLVED] m-dependent stationary process

Hi all

Could you tell me a strict mathematical definition of "m-dependent stationary process" or maybe a link to where I could find it

Thanks In Advance

 

[EnumaElish]

The stationary sequence X1, X2, ... is said to be m-dependent if Xs and Xt are independent whenever |s - t| > m.

https://www.amazon.com/gp/product/0824782534/?tag=pfamazon01-20.

 

[New_Galatea]

Thank you very much

 

[New_Galatea]

And may be you know what is the dependence between m-dependent stationary process (where m=q) and ARMA(0,q) process?

 

[EnumaElish]

Loosely, ARMA(0,q) = AR(0) + MA(q) = MA(q) which is X_t = \epsilon_t + \sum_{i=1}^m \theta_i \epsilon_{t-i} (since q = m). See this link. You should be able to work out what this implies for m-dep. stat. process. (Hint: are Xt and Xs dependent or independent when t - s > m?)