In two recent papers, Granger and Ding (1995a,b) considered long retur
n series that are first differences of logarithmed price series or pri
ce indices. They established a set of temporal and distributional prop
erties for such series and suggested that the returns are well. charac
terized by the double exponential distribution. The present paper show
s that a mixture of normal variables with zero mean can generate serie
s with most of the properties Granger and Ding singled out. In that ca
se, the temporal higher-order dependence observed in return series may
be described by a hidden Markov model. Such a model is estimated for
ten subseries of the well-known S&P 500 return series of about 17,000
daily observations. It reproduces the stylized facts of Granger and Di
ng quite well, but the parameter estimates of the model sometimes vary
considerably from one subseries to the next. The implications of thes
e results are discussed. (C) 1998 John Wiley & Sons, Ltd.