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 themselves, but the power transformation of the absolute return ¦r_t¦^d also has quite high autocorrelation for long lags. It is possible to characterize ¦r_t¦^d 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 δ of the heteroskedasticity equation to be estimated from the data.