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Time series understanding a proposition

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Proposition: If C(0)>0 and C(h)->0 as h-> infinity, then the covariance matrix gamma_n =[c(i-j)] for i,j- 1,2,....n of (x_!,....x_x)' is non singular for every n.

    I want to convince myself that the converse is not true. (ie I want a counter example of a stationary process {x_t} such that Ganna_n is nonsingular for all n and c(h)-/->0 as h->infinity
    2. Relevant equations



    3. The attempt at a solution
    I am not sure how to construct such a counter example.
     
  2. jcsd
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