Covariogram estimation for the process contaminated with linear trend

1. Jan 27, 2007

New_Galatea

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. Jan 27, 2007

EnumaElish

What is a covariogram?

3. Jan 28, 2007

New_Galatea

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.

4. Jan 28, 2007

EnumaElish

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

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