  This paper proposes strategies to detect time reversibility in stationary
stochastic processes by using the properties of mixed causal and noncausal
models. It shows that they can also be used for non-stationary processes when
the trend component is computed with the Hodrick-Prescott filter rendering a
time-reversible closed-form solution. This paper also links the concept of an
environmental tipping point to the statistical property of time irreversibility
and assesses fourteen climate indicators. We find evidence of time
irreversibility in $GHG$ emissions, global temperature, global sea levels, sea
ice area, and some natural oscillation indices. While not conclusive, our
findings urge the implementation of correction policies to avoid the worst
consequences of climate change and not miss the opportunity window, which might
still be available, despite closing quickly.
