# Is the absolute value of a stationary series also stationary?

I know that linear transformations of time series arising from (weakly) stationary processes are also stationary. Is this true, however, for a transformation of a series via taking the absolute value of each element as well? In other words, if $${xi,i∈N}\{x_i,i\in\mathbb{N}\}$$ is stationary, then is $${|xi|,i∈N}\{|x_i|,i\in\mathbb{N}\}$$ stationary as well?