What Is an M-Dependent Stationary Process?

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Discussion Overview

The discussion revolves around the definition and properties of an "m-dependent stationary process," exploring its mathematical characterization and its relationship to ARMA(0,q) processes. The scope includes theoretical definitions and potential connections between different statistical models.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant requests a strict mathematical definition of "m-dependent stationary process."
  • Another participant defines an m-dependent stationary process as one where Xs and Xt are independent whenever |s - t| > m.
  • A participant inquires about the relationship between m-dependent stationary processes (where m=q) and ARMA(0,q) processes.
  • Another participant suggests that ARMA(0,q) can be expressed as a combination of AR(0) and MA(q) processes, and hints at exploring the implications for m-dependent stationary processes.

Areas of Agreement / Disagreement

Participants provide differing perspectives on the relationship between m-dependent stationary processes and ARMA models, indicating that the discussion remains unresolved regarding the implications of these relationships.

Contextual Notes

There are assumptions regarding the definitions of independence and dependence in the context of m-dependent processes and ARMA models that are not fully explored. The implications of the hints provided are also not fully resolved.

New_Galatea
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[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
 
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Thank you very much
 
And may be you know what is the dependence between m-dependent stationary process (where m=q) and ARMA(0,q) process?
 
Loosely, ARMA(0,q) = AR(0) + MA(q) = MA(q) which is [itex]X_t = \epsilon_t + \sum_{i=1}^m \theta_i \epsilon_{t-i}[/itex] (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?)
 
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