Relationship between PACF and ACF of MA(1) AND AR(1)

Discussion in 'CS2' started by Molly, Aug 11, 2022.

  1. Molly

    Molly Ton up Member

    Hi all,

    am struggling on this part of the CMP chapter 13 - time series 1 "the PACF of an MA(1) process behaves like the ACF of an AR(1) process, and the PACF of an AR(1) process behaves like the ACF of an MA(1) process"

    It sounds like this is fairly obvious, but i dont understand why this is the case. Can anyone explain please?

    Thanks so much
     
  2. Andrew Martin

    Andrew Martin ActEd Tutor Staff Member

    Hi Molly

    The key results we have for these processes are:

    The ACF of an MA(1) process cuts off after lag 1
    The PACF of an MA(1) process decays approximately geometrically to 0

    The ACF of an AR(1) process decays geometrically to 0
    The PACF of an AR(1) process cuts off after lag 1

    So the comment is just referring to the opposite results we have for the ACF / PACF of these processes.

    Hope this helps!

    Andy
     
    Molly likes this.
  3. Molly

    Molly Ton up Member

    Thats amazing thanks so much Andy!!!
     

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