1
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ How is Hurst exponent related to stationarity and mean reversion? $\endgroup$ – Richard Hardy May 30 '15 at 14:31
  • $\begingroup$ Are you clear on the mean reversion concept now? $\endgroup$ – Brethlosze May 30 '15 at 19:43
4
$\begingroup$

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.

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.