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We use new and established methodologies in multivariate time series analysisto study the dynamics of 414 Australian hydrological stations' streamflow.First, we analyze our collection of time series in the temporal domain, andcompare the similarity in hydrological stations' candidate trajectories. Then,we introduce a Whittle Likelihood-based optimization framework to study thecollective 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 hydrologicalstreamflow process across Australia. To determine the stability of suchbehaviours over time, we then study the evolution of the governing dynamics andunderlying time series with time-varying applications of principal componentsanalysis (PCA) and spectral analysis.

Temporal and spectral governing dynamics of Australian hydrological streamflow time series