A Time-Series Model of Stock Returns with a Positive Short-Term Correlation and a Negative Long-Term Correlation

We study portfolio stock return behavior that exhibits both a positive autocorrelation over short horizons and a negative autocorrelation over long horizons. 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. 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.