A Long Memory Property of Stock Market Returns and a New Model

A ‘long memory ’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns them-selves, but the power transformation of the absolute return lrfl ” also has quite high autocorrel-ation for long lags. It is possible to characterize lrfld to be ‘long memory ’ and this property is strongest when d is around 1. This result appears to argue against ARCH type specifications based upon squared returns. But our Monte-Carlo study shows that both ARCH type models based on squared returns and those based on absolute return can produce this property. A new general class of models is proposed which allows the power…