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In the past decades, time series analysis tools and techniques have allowed us to investigate in detail the statistical and dynamical features of complex real-world systems based on observed data, and formulate insights regarding the underlying physical processes. However, most of these methods do not have the capacity to accommodate inherent spatial and temporal variabilities, or imprecision in measurements in the form of uncertainties. There is a lack of a clear framework that begins with a proper description of the uncertainties in the data (due to spatio-temporal variability or due to imprecision) and propagates these uncertainties throughout the rest of the analysis till the final inferences. The development of such a framework will find use in several disciplines, ranging from climate to neuroscience to finance to medicine. Particularly, in the field of climate, where spatial and temporal variabilities are of paramount importance, this is the next logical step to extend the field of time series analysis in this direction. This would also have crucial repercussions in the field of paleoclimate data analysis, as in the context of paleoclimate datasets, it is more useful to represent paleoclimate proxy time series as having associated uncertainties of estimation that primarily arise due to an imprecision in the dating of the paleoclimate proxy archives.