We introduce a long-memory dynamic Tobit model, defining it as a
censored version of a fractionally-integrated Gaussian ARMA model,
which may include seasonal components and/or additional regression
variables. Parameter estimation for such a model using standard
techniques is typically infeasible, since the model is not
Markovian, cannot be expressed in a finite-dimensional state-space
form, and includes censored observations. Furthermore, the
long-memory property renders a standard Gibbs sampling scheme
impractical. Therefore we introduce a new Markov chain Monte Carlo
sampling scheme, which is orders of magnitude more efficient than
the standard Gibbs sampler. The method is inherently capable of
handling missing observations. In case studies, the model is fit to
two time series: one consisting of volumes of requests to a hard
disk over time, and the other consisting of hourly rainfall
measurements in Edinburgh over a two-year period. The resulting
posterior distributions for the fractional differencing parameter
demonstrate, for these two time series, the importance of the
long-memory structure in the models.