  In this article we describe a new Hermite series based sequential estimator
for the Spearman's rank correlation coefficient and provide algorithms
applicable in both the stationary and non-stationary settings. To treat the
non-stationary setting, we introduce a novel, exponentially weighted estimator
for the Spearman's rank correlation, which allows the local nonparametric
correlation of a bivariate data stream to be tracked. To the best of our
knowledge this is the first algorithm to be proposed for estimating a
time-varying Spearman's rank correlation that does not rely on a moving window
approach. We explore the practical effectiveness of the Hermite series based
estimators through real data and simulation studies demonstrating good
practical performance. The simulation studies in particular reveal competitive
performance compared to an existing algorithm. The potential applications of
this work are manifold. The Hermite series based Spearman's rank correlation
estimator can be applied to fast and robust online calculation of correlation
which may vary over time. Possible machine learning applications include,
amongst others, fast feature selection and hierarchical clustering on massive
data sets.
