  House price increases have been steady over much of the last 40 years, but
there have been occasional declines, most notably in the recent housing bust
that started around 2007, on the heels of the preceding housing bubble. We
introduce a novel growth model that is motivated by time-warping models in
functional data analysis and includes a nonmonotone time-warping component that
allows the inclusion and description of boom-bust cycles and facilitates
insights into the dynamics of asset bubbles. The underlying idea is to model
longitudinal growth trajectories for house prices and other phenomena, where
temporal setbacks and deflation may be encountered, by decomposing such
trajectories into two components. A first component corresponds to underlying
steady growth driven by inflation that anchors the observed trajectories on a
simple first order linear differential equation, while a second boom-bust
component is implemented as time warping. Time warping is a commonly
encountered phenomenon and reflects random variation along the time axis. Our
approach to time warping is more general than previous approaches by admitting
the inclusion of nonmonotone warping functions. The anchoring of the
trajectories on an underlying linear dynamic system also makes the time-warping
component identifiable and enables straightforward estimation procedures for
all model components. The application to the dynamics of housing prices as
observed for 19 metropolitan areas in the U.S. from December 1998 to July 2013
reveals that the time setbacks corresponding to nonmonotone time warping vary
substantially across markets and we find indications that they are related to
market-specific growth rates.
