  The estimation of entropy rates for stationary discrete-valued stochastic
processes is a well studied problem in information theory. However, estimating
the entropy rate for stationary continuous-valued stochastic processes has not
received as much attention. In fact, many current techniques are not able to
accurately estimate or characterise the complexity of the differential entropy
rate for strongly correlated processes, such as Fractional Gaussian Noise and
ARFIMA(0,d,0). To the point that some cannot even detect the trend of the
entropy rate, e.g. when it increases/decreases, maximum, or asymptotic trends,
as a function of their Hurst parameter. However, a recently developed technique
provides accurate estimates at a high computational cost. In this paper, we
define a robust technique for non-parametrically estimating the differential
entropy rate of a continuous valued stochastic process from observed data, by
making an explicit link between the differential entropy rate and the Shannon
entropy rate of a quantised version of the original data. Estimation is
performed by a Shannon entropy rate estimator, and then converted to a
differential entropy rate estimate. We show that this technique inherits many
important statistical properties from the Shannon entropy rate estimator. The
estimator is able to provide better estimates than the defined relative
measures and much quicker estimates than known absolute measures, for strongly
correlated processes. Finally, we analyse the complexity of the estimation
technique and test the robustness to non-stationarity, and show that none of
the current techniques are robust to non-stationarity, even if they are robust
to strong correlations.
