# Thread: Stationary process of time series

1. ## Stationary process of time series

Say we have $X_t$ = $\sum_{j=1}^{q}(A_j cos\lambda_jt + B_j sin\lambda_jt)$ for t = 0,1,2...

where $\lambda_1,....\lambda_q$ are constants and $A_1,...A_q,B_1,...B_q$ are independent, zero mean r.v's all with variance $\sigma^2$.

I need to show that $X_t$ is a stationary process. I've already worked out the mean, but now I just need to show that Cov( $X_t,X_{t+k}$) depends only on k, and is independent of t.

Any help would be much appreciated.