Subject CT6, September 2015, Question 11

Discussion in 'CS2' started by Molly, Sep 14, 2022.

  1. Molly

    Molly Ton up Member

    Hi all,

    I'm really confused on this question. I have seen the basic examples of how an AR(3) process can be written in matrix form. I just have absolutely no idea whats going on with this one! how was the matrix formed?

    Any help is really appreciated

    Thanks
     
  2. Andrew Martin

    Andrew Martin ActEd Tutor Staff Member

    Hi Molly

    Which part of the question are you looking at, part (i) or part (ii)?

    Andy
     
  3. Molly

    Molly Ton up Member

    Hi Andy,

    sorry i should have said in my question, im looking at part (i), i dont understand how to get those equations into matrix form and can't find anything helpful on youtube!

    Thanks
     
  4. Andrew Martin

    Andrew Martin ActEd Tutor Staff Member

    Hi Molly

    As the aim is to have M(Z_t) = N(Z_t-1) + e_t where Z_t = (Xt, Yt), it's probably a good idea for us to rearrange the equations to have terms at time t on the LHS and terms at time t-1 on the RHS. So:

    Xt - beta Yt = 0.5 Xt-1 + et1
    Yt - beta Xt = 0.5 Yt-1 + et2

    We can write these two equations in matrix form as:

    M(Z_t) = N(Z_t-1) + e_t

    where:
    M =
    1 -beta
    -beta 1

    N =
    0.5 0
    0 0.5

    multiple out the matrix equation to check it's the same.

    Hope this helps!

    Andy
     
    Molly likes this.
  5. Molly

    Molly Ton up Member

    that does help hugely, thank you
     

Share This Page