  We use new and established methodologies in multivariate time series analysis
to study the dynamics of 414 Australian hydrological stations' streamflow.
First, we analyze our collection of time series in the temporal domain, and
compare the similarity in hydrological stations' candidate trajectories. Then,
we introduce a Whittle Likelihood-based optimization framework to study the
collective similarity in periodic phenomena among our collection of stations.
Having identified noteworthy similarity in the temporal and spectral domains,
we introduce an algorithmic procedure to estimate a governing hydrological
streamflow process across Australia. To determine the stability of such
behaviours over time, we then study the evolution of the governing dynamics and
underlying time series with time-varying applications of principal components
analysis (PCA) and spectral analysis.
