Stability and lack of memory of the returns of the Hang Seng index

In this paper we show that the logarithmic returns of the Hang Seng index from January 2, 1987 to November 14, 2005 statistically resemble a sequence of independent identically distributed Lévy stable random variables. This is in stark contrast to Xiu and Jin (2007) [39], where long-memory FARIMA processes with Gaussian noise were suggested as well fitted to the data. The lack of memory is checked by using Lo’s modified R / S statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean-squared displacement. In order to test stability of the data we employ several statistical tests based on the empirical distribution function. Finally, we also show that the returns possess no conditional heteroscedasticity property thus excluding the ARCH/GARCH family of processes as possible underlying models.