If $X(t)$ is WSS with autocorrelation $R_{X}(\tau)$ then is $Y(t)=X(-t)$ WSS? How to find Cross Correaltion of $X(t)$ and $Y(t)$ too? And, can we say they are jointly WSS?
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A process $X_t$ is WSS when ($K_{XX}$ is an autocovariance function):
$$ \forall\tau\in\mathbb{R}: \mathbb{E}[X_t]=\mathbb{E}[X_{t+\tau}] $$ $$ \forall t_1,t_2\in\mathbb{R}:K_{XX}(t_1, t_2)=K_{XX}(t_1-t_2,0) $$ $$ \forall t\in\mathbb{R}:\mathbb{E}[|X_t|^2] < \infty $$
You can note, that this definition is symmetric with respect to substitution $t\rightarrow -t$, so inverted process is WSS if and only if the original one is WSS.
