  Price range contains important information about the asset volatility, and
has long been considered an important indicator for it. In this paper, we
propose to jointly model the [low, high] price range as a random interval and
introduce an interval-valued GARCH (Int-GARCH) model for the corresponding
[low, high] return range process. Model properties are presented under the
general framework of random sets, and the parameters are estimated by a
metric-based conditional least squares (CLS) method. Our empirical analysis of
the daily return range data of Dow Jones component stocks yields very
interesting results.
