If I have a time series that exhibits mean reverting properties, does it necessarily mean that the time series is mean stationary?
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As pointed out by Brian, the question is vague because generally mean reversion requires a well defined mean. Nevertheless, there are processes which are not mean stationary (mean is not homogenous across observations) for which a concept of mean exists. Let $\mu_t = E(x_t)$. In general you can have $\mu_t \neq \mu_s$ (i.e. violate mean stationarity) but have a well defined long run mean, i.e. the limit $$\frac1n \sum_{t=1}^n \mu_t \to \bar \mu$$ exists. In such a situation, you can define a concept of mean reversion to the long run mean that applies to non mean stationary processes. |
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