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Covariogram estimation for the process contaminated with linear trend

  1. Jan 27, 2007 #1
    Let {S(t), t=1,2,...} be a zero-mean, unit variance, second-order stationary process in R^1,
    and define Y(t)=S(t)+k(t-(n+1)/2), t=1,2,...,n.
    Then the process Y(t) is not second-order stationary process since it is contaminated with linear trend, k – degree of contamination.

    Define R(h) – covariogram for Y(t) process and
    Define Rs(h) - covariogram for S(t) process.

    Could you help me to show that estimate of R(h) converges in probability to estimate of Rs(h) + ((k^2) * (n^2))/12

    Thank in advance
     
  2. jcsd
  3. Jan 27, 2007 #2

    EnumaElish

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    What is a covariogram?
     
  4. Jan 28, 2007 #3
    As I know “Covariogram” is synonym of “Covariance”.
    A strict definition is following:
    Let x(t) be a spatial process. Covariogram for spatial process x(t) is a function
    R(t1,t2)= M[(x(t1)-Mx(t1))(x(t2)-Mx(t2))].
    Here M – symbol of mean.
     
  5. Jan 28, 2007 #4

    EnumaElish

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    Have you attempted a solution? Is there a specific obstacle you cannot get around?
     
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