The economic question is basic. Does leverage behave like a random walk? Does leverage mean revert?
It is well known that if something is measured with error, then on average the error term washes out subsequently, creating one possible source of reversion. But it is far from the only possible source of mean reverting behavior. The underlying corporate cash flows could mean revert, or the managers could take offsetting actions. In fact there is direct evidence of off-setting issuing activity. How big it is, and how fast it is are debated. But it is there in the data.
Go to FINRA (http://cxa.marketwatch.com/finra/MarketData/Default.aspx) and extract the debt issues. Then go to SDC and extract the issuing data. That will give you actual security issues by real firms.
Then go to Compustat (or to Edgar and get the annual reports balance sheets if you really think that Compustat is too error prone). Calculate the leverage ratios for say the S&P 500 firms. Then examine the patterns in the subsequent issuing decisions and study whether, and how those issues are related to the leverage ratios -- and other factors. Then come back and tell us whether you still believe that it is all just a statistical regression to the mean.
Cheap and easy simulation can illustrate that something is logically possible. It does not show that other things are not.