Necessity of negative serial correlation for mean-reversion of stock prices

In this paper, we show that the widespread common perception that stock returns must necessarily exhibit negative first-order autocorrelation for the mean-reverting components of stock prices is not quite correct. The necessity of negative autocorrelation in one-period returns is an artifact of assuming an AR(1) process for the transitory components of the underlying stock price and assuming independence between innovations in the transitory process and innovations in the permanent components. The sign of first-order return autocorrelation for mean-reverting property could be positive under a different lag structure of the transitory components of stock prices.