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Analysis of thickness time series, generated from varved sediments originating from lakes in the Arctic, USA, Finland, Germany and Poland, and intermittently spanning the last ca. 15,000 cal yrs BP, reveals a range of system dynamics. Lake sedimentation leading to varve formation can be considered in terms of the quantity and stratigraphic position of the sedimentary deposit. The amount of sediment deposited is statistically represented by gamma and log-normal distributions. This suggests sedimentation is characterised by a series of random depositional events that are added and multiplied over time, respectively. Phase portraits qualitatively indicate scale invariance. Power spectra, autocorrelation functions and fluctuation analysis quantitatively confirm scale invariance over all resolvable orders of magnitude, with exponents in the range ca. H = 0.6 to 0.9. Crossovers occur in the power spectra on ca. 100 yrs timescales for some lakes, indicating the possible presence of changes in dominant timescales of large scale climatic processes. Deviations from established relations between scaling exponents, and differences from the AR(1) null hypothesis, both based on random walk processes, indicate the role of other underlying scaling mechanisms, such as (self-organised) critical phenomena and/or multiscaling. E-folding times calculated from waiting time analysis indicates lake systems are characterised by two states, characterising the ''main" dynamics on decadal timescales, and the ''extreme" dynamics up to centennial timescales. The e-folding times for the main system processes compare well with some of those calculated from the autocorrelation function and AR(1) process, again indicating the presence of other complex dynamics. Effectively, lakes are threshold systems with random forcing on different timescales. No relations were isolated for correlations between basic physical parameters and statistical exponents, indicating the individualistic nature of lake systems. This is confirmed by the lack of spatial correlation between averaged, but unshifted lake systems. This is attributed to insufficient atmospheric spatiotemporal smoothing, the thermal regime of lakes displaying a greater response to slower long term processes, rather than faster shorter term processes, and to the occurrence of extreme events, which ultimately control the emergence of correlation, up to and beyond centennial timescales.