# Time Series: Does stationarity imply mean reversion?

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?

• How is Hurst exponent related to stationarity and mean reversion? – Richard Hardy May 30 '15 at 14:31
• Are you clear on the mean reversion concept now? – Brethlosze May 30 '15 at 19:43

## 1 Answer

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.

• Then how can I test for mean reversion? – user1691278 May 31 '15 at 6:54