# Autocovariance of a particular process, tX

Given the following stochastic process:

$$Y_t = t X$$

where: $E(X)=0$ and $VAR(X) = 1$.

Is it correct to obtain the autocovariance in the following way?

$$COV(Y_t, Y_s) = E [Y_tY_s] ~~~~~~~~~~~~~~~~~~~\text{since, E[X_t] = 0.}$$

$$E [Y_tY_s]=E[tXsX] = tsE[X^2] = tsVAR(X) = ts$$

Others say me that the correct way is:

$$E [Y_tY_s]=E[tXsX] = tE[X]sE[X] = 0$$

Which one is correct?

• Perhaps something to note too is that this process is not stationary, and an auto-covariance function that depends only on the lag (i.e. $t-s$) does not exist. Jan 26 '17 at 2:43