# Easy (?) question regarding Mean Reversion / Persistence

#### rtd

##### New Member
Hi all,

I am doing a simple regression with accounting data. I regress current earnings (E_t) on the earnings of the previous periods, i.e. estimate persistence:

E_t = y0 + y1 * E_t-1 + y2 * E_t-2 + y3 * E_t-3 + Errorterm

I know that a coefficient below 1 indicates mean reversion. I have two sub-samples. In the first the coefficients decrease monotonously, even below zero in t-3. In the other sub-sample the coefficient in t-3 increases compared to t-2.

How would you interpret these results? What is the implication of a negative coefficient? Is anything of this a sign, that mean reversion actually takes place in period t-3?

I appreciate any input! Thanks alot in advance!
Michael

#### PeterVincent

##### New Member
Hi Michael,

When you have sorted this out would you please post your intrepretation here.

Peter

#### rtd

##### New Member
Hi Peter,

what I have found out so far:

- A coefficient of 1 indicates a random walk

- If the coefficient is smaller (below 1) the mean reversion happens quicker and the process has a lower std. dev.

- This continues to -1 and the change of sign at zero does not seem to have any obvious influence, at least not from my simulations of a timeseries in excel

- above/below 1/-1 the process goes exponential through the roof

What i do not really understand is the difference between two timeseries with the following coefficients:

t-1;t-2;t-3
0.6;0.3;0.1
0.6;0.1;0.3

For the second series the t-2 value does not really seem to play an important role, just like the t-3 value for the first series.

I am not sure what this means in a context where you would theretically expect monotonously decreasing coefficients for higher order variables.

Are you working on a specific topic (PhD?)?
Thanks!

#### PeterVincent

##### New Member
Hi Michael,
Thanks for the information.

I am trying to learn about statistics by reading stuff on the forum and answering where possible, I also post looking for assistance.

Your problem interested me because I do not have a clue what you were on about and I wanted to find out more. I know what regression means but not persistence, mean reversion, sub-samples and decrease monotonously.

There was a post on the forum from a chap who wanted to examine his crossword times and I was wondering what the regression of current time on previous time might show up.

Regards,

Peter