stylized facts of daily return series

by Tobias Ryden, Timo Terasvirta and Stefan Asbrink

they considered long return series that are first differences of logarithmed price series or price indices. they established a set of temporal and distributional properties for such series, and sugested that returns are well characterized by double exponential distribution.
This paper shows that a mixture of mean zero normal variables can generate series with most of the properties Granger and Ding singled out. In that case, the temporal higher order dependence observed in return series may be described by an HMM.