Abstract

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 turn |rt|d also has quite high autocorrelation for long lags. It is possible to characterize |rt|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.

INTRODUCTION

If rt is the return from a speculative asset such as a bond or stock, this paper considers the temporal properties of the functions |rt|d for positive values of d. It is well known that the returns themselves contain little serial correlation, in agreement with the efficient market theory. However, Taylor (1986) found that |rt| has significant positive serial correlation over long lags. This property is examined on long daily stock market price series. It is possible to characterize |rt|d to be “longmemory”, with quite high autocorrelations for long lags. It is also found, as an empirical fact, that this property is strongest for d = 1 or near 1 compared to both smaller and larger positive values of d.