  Discrimination between non-stationarity and long-range dependency is a
difficult and long-standing issue in modelling financial time series. This
paper uses an adaptive spectral technique which jointly models the
non-stationarity and dependency of financial time series in a non-parametric
fashion assuming that the time series consists of a finite, but unknown number,
of locally stationary processes, the locations of which are also unknown. The
model allows a non-parametric estimate of the dependency structure by modelling
the auto-covariance function in the spectral domain. All our estimates are made
within a Bayesian framework where we use aReversible Jump Markov Chain Monte
Carlo algorithm for inference. We study the frequentist properties of our
estimates via a simulation study, and present a novel way of generating time
series data from a nonparametric spectrum. Results indicate that our techniques
perform well across a range of data generating processes. We apply our method
to a number of real examples and our results indicate that several financial
time series exhibit both long-range dependency and non-stationarity.
