  Motivated by the modeling of liquidity risk in fund management in a dynamic
setting, we propose and investigate a class of time series models with
generalized Pareto marginals: the autoregressive generalized Pareto process
(ARGP), a modified ARGP (MARGP) and a thresholded ARGP (TARGP). These models
are able to capture key data features apparent in fund liquidity data and
reflect the underlying phenomena via easily interpreted, low-dimensional model
parameters. We establish stationarity and ergodicity, provide a link to the
class of shot-noise processes, and determine the associated interarrival
distributions for exceedances. Moreover, we provide estimators for all relevant
model parameters and establish consistency and asymptotic normality for all
estimators (except the threshold parameter, which as usual must be dealt with
separately). Finally, we illustrate our approach using real-world fund
redemption data, and we discuss the goodness-of-fit of the estimated models.
