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Background: In this work, we implement a data-driven approach using an aggregation of several analytical methods to study the characteristics of COVID-19 daily infection and death time series and identify correlations and characteristic trends that can be corroborated to the time evolution of this disease. The datasets cover twelve distinct countries across six continents, from January 22, 2020 till March 1, 2022. This time span is partitioned into three windows: (1) pre-vaccine, (2) post-vaccine and pre-omicron (BA.1 variant), and (3) post-vaccine including post-omicron variant. This study enables deriving insights into intriguing questions related to the science of system dynamics pertaining to COVID-19 evolution. Methods: We implement a set of several distinct analytical methods for: (a) statistical studies to estimate the skewness and kurtosis of the data distributions; (b) analyzing the stationarity properties of these time series using the Augmented Dickey-Fuller (ADF) tests; (c) examining co-integration properties for the non-stationary time series using the Phillips-Ouliaris (PO) tests; (d) calculating the Hurst exponent using the rescaled-range (R/S) analysis, along with the Detrended Fluctuation Analysis (DFA), for self-affinity studies of the evolving dynamical datasets. Results: We notably observe a significant asymmetry of distributions shows from skewness and the presence of heavy tails is noted from kurtosis. The daily infection and death data are, by and large, nonstationary, while their corresponding log return values render stationarity. The self-affinity studies through the Hurst exponents and DFA exhibit intriguing local changes over time. These changes can be attributed to the underlying dynamics of state transitions, especially from a random state to either mean-reversion or long-range memory/persistence states. Conclusions: We conduct systematic studies covering a widely diverse time series datasets of the daily infections and deaths during the evolution of the COVID-19 pandemic. We demonstrate the merit of a multiple analytics frameworks through systematically laying down a methodological structure for analyses and quantitatively examining the evolution of the daily COVID-19 infection and death cases. This methodology builds a capability for tracking dynamically evolving states pertaining to critical problems. [ABSTRACT FROM AUTHOR]