  We propose a novel noninvasive method, based on extreme value theory, to
decide whether a given stationary time series $x(\tau)$ is at equilibrium or
not. This technique does not require detailed knowledge of the system dynamics.
Our method relies on the distribution $P(t_{\rm m}|T)$ of the time $t_{\rm m}$
at which $x(\tau)$ reaches its maximal value in $[0,T]$. We show that if the
underlying process is at equilibrium, then $P(t_{\rm m}|T)$ is symmetric around
$t_{\rm m}=T/2$, i.e., $P(t_{\rm m}|T)=P(T-t_{\rm m}|T)$. Thus, if $P(t_{\rm
m}|T)$ is not symmetric the process is necessarily out-of-equilibrium. We
illustrate this principle by exact solutions in a number of equilibrium and
nonequilibrium stationary processes. For a large class of equilibrium
stationary processes that correspond to diffusion in a confining potential, we
show that the scaled symmetric distribution $P(t_{\rm m}|T)$, for large $T$,
has a universal form (independent of the details of the potential). This
universal distribution is uniform in the "bulk", i.e., for $0 \ll t_{\rm m} \ll
T$ and has a nontrivial edge scaling behavior for $t_{\rm m} \to 0$ (and when
$t_{\rm m} \to T$), that we compute exactly.
