Covariogram estimation for the process contaminated with linear trend

  • #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
 

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