# Does shift-invariance of a measure in ergodic theory imply this?

I am a little confused and would appreciate some elaboration on this. Let $$\mu$$ be a measure on $$\mathbb{R}$$ equipped with the Borel $$\sigma$$-algebra $$\mathcal{B}(\mathbb{R})$$. Then the translation invariance property of $$\mu$$ means that $$$$\forall y \in\mathbb{R},\quad\forall B\in\mathcal{B},\quad \mu(y+B)=\mu(B)$$$$ Now let's say we have the stochastic series $$\{x_1,x_2,\cdots,x_T\}$$ is a Markov process. Would a transformation of the sort $$\{\tilde{x}_1,\tilde{x}_2,\cdots,\tilde{x}_T\}$$, where $$\tilde{x}_i=x_i+y_i$$ for $$y_i\in \mathbb{R}$$ for $$i=1,\cdots,T$$ imply that $$\{\tilde{x}_1,\tilde{x}_2,\cdots,\tilde{x}_T\}$$ also is a Markov process?