We study stock return behavior that exhibits both a positive autocorrelation over
short horizons and a negative autocorrelation over long horizons, which has been a
focus of many recent theoretical studies of stock price. These autocorrelations are
more significant in small size portfolios. Among various forms of temporary
components in stock prices, an AR(2) component is the simplest model compatible with
this pattern of returns, which yields an ARMA (2,2) model of stock returns. We show
that the significance of this model is that it requires the presence of feedback
trading, which is a form of irrational trades, and the market’s slow adjustment to
the market fundamentals, which is consistent with recent modelings of stock prices.
A Kalman filter is used to estimate each unobservable component in exploring the
relationship between the firm size and the autocorrelation. We find that the
variation of the temporary component becomes greater as the firm size gets smaller.
This implies that the deviation from the market fundamentals is larger in small size
portfolios than in large size portfolios.

