TAILIEUCHUNG - A long memory property of stock market returns and a new model*

On balance, it is desirable to have a diversified and balanced financial system where both financial intermediaries and financial markets play important roles in imparting greater competitiveness and efficiency to the financial system. In the present context of financial liberalisation, stock markets and banks emerge as sources of corporate finance and stock market development actually tends to increase the quantity of bank loans through improved debt- equity ratios. Thus, the coexistence of both systems is socially desirable not only because it encourages competition, but also because it reduces transaction costs within the financial system, and helps improve resource allocation within the. | Journal of Empirical Finance 1 1993 83-106. North-Holland A long memory property of stock market returns and a new model Zhuanxin Ding Clive . Granger and Robert F. Engle University of California San Diego CA USA Received June 1992. Final version accepted February 1993 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 return rz rf also has quite high autocorrelation for long lags. It is possible to characterize r 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 Ỗ of the heteroskedasticity equation to be estimated from the data. 1. 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 I r 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 I r I has significant positive serial correlation over long lags. This property is examined on long daily stock market price series. It is possible to characterize I rt Id to be long-memory 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. This result appears to argue against ARCH type specifications based upon squared returns. The paper examines whether various classes of models are consistent with this observation. A new general class of models is then .

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