There is a unique case where a
regression of a nonstationary series on another nonstationary series does not
result in spurious regression. This is the situation of cointegration. If two
time series have stochastic trends (i.e. they are nonstationary), a regression
of one on the other may cancel out the stochastic trends, which may suggest
that there is a long-run, or equilibrium, relationship, between them, even
though individually the two series are nonstationary.
Keep in mind that unit
root and nonstationarity are not synonymous. A stochastic process with a
deterministic trend is nonstationary but not unit root[1].
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