Solved – Time Series: Does stationarity imply mean reversion

Question

I'm trying to see if a time series demonstrates mean reversion. I found two tests: Augmented Dickey Fuller Test and Hurst Exponent. However, the alternative hypothesis is that the series is stationary. Does stationarity, then, imply mean reversion?

Answer 1

Define $X_t = X_{t-1}$ for $t>0$. Let $X_0$ take the value $1$ with probability $0.5$ and $0$ otherwise. $X$ is then stationary but not mean reverting. Thus, stationarity does not imply mean reversion.