Testing for mean reversion ADF test

[Maurelius]

Hi!

I am a student and I'm doing a study whether the Swedish stock market are mean reverting or "follows" a random walk. I found this forum when searching for help and it was very helpful, but there's still a few questionmarks that needs to be cleared. Since I'm quite new to all of this it would be great to have it explained by all of you experts here on the forum :)

A brief info on our study:
We have collected daily data for the last 15 years of 75 individual stocks and also an index. (This means over 3000 observations for each stock)
We want to test whether there is any predictability in case of mean reversion during this time or if it simply "follows" random walk.

So what we would love some help with is how to, step-by-step, use and interpret the ADF test in our case.

According to bensamen this is how you do:
1. Estimate the most general model with trend and intercept. And then check the stationarity on the first part of the output. If the data is non-stationary (i.e. the computed absolute t-statistic is smaller than the absolute critical value or the prob is > 5% ), then you need to check on the second part of the output whether the trend coefficient (@trend) is significant or not.
- If the @trend is significant, you can conclude that you have data with deterministic trend. To have it stationary, you can use either Trend-Stationary Process (TSP) or Difference-Stationary Process (DSP). To differentiate, all you have to do is to choose "1st difference" for the ADF test, right?
- If the @trend isnot significant, then you have to estimate the model with intercept.
2. If the model with intercept is non-stationary, you can at least to check the constant term to be sure if you have a stochastic trend with constant or not.
3. Lastly, you can use the none model.
PS. 1. The data generate by a stochastic trend are stationary only by using Difference-Stationary Process (DSP).
2. After having a deterministic trend stationary using Trend-Stationary Process (TSP), you dont have to check its stationary with the full model (with intercept and trend).

But when is it necessary to differentiate a model? And is that important in our case?

If, let's say, we can reject the null hypthesis, does that "automatically" tell us a stock is mean reverting? Or do we have to look at e.g the Durbin-Watson stat to know if it shows negative autocorrelation (=mean reversion)?

Also, how can you tell the mean reverting speed?

I would really love all the help I can get! If possible, we could share the data we're working with if it's easier for you to help, but let me know if that's necessary.

Thanks in advance!

[Maurelius]

So after a lot of reading on the topic I've managed to figure out the step-by-step test for random walk with trend+intercept, intercept only or none. But the big question now is; if I can reject the null hypothesis, does that automatically mean that the time series are mean reverting? Or how should I interpret this? Do I need to look at e.g the Durbin Watson stat for autocorrelation?

[Maurelius]

Please, anyone who can help me with this? I really need to know and I would really appreciate if anyone could tell me.