A natural ∼1450-yr global Holocene climate periodicity underlies a portion of the present global warming trend. Calibrated basal radiocarbon dates from 71 paludified peatlands across the western interior of Canada demonstrate that this periodicity regulated western Canadian peatland initiation. Peatlands, the largest terrestrial carbon pool, and their carbon-budgets are sensitive to hydrological fluctuations. The global atmospheric carbon-budget experienced corresponding fluctuations, as recorded in the Holocene atmospheric CO2 record from Taylor Dome, Antarctica. While the climate changes following this ∼1450-yr periodicity were sufficient to affect the global carbon-budget, the resultant atmospheric CO2 fluctuations did not cause a runaway climate–CO2 feedback loop. This demonstrates that global carbon-budgets are sensitive to small climatic fluctuations; thus international agreements on greenhouse gasses need to take into account the natural carbon-budget imbalance of regions with large climatically sensitive carbon pools.

We use a new statistical test based on the signal coherence function to detect subtle periodicities in the Chilean exchange rate. We resort to a unique intraday data set that allows us to capture persistent cyclical movements during the day that challenge the random walk hypothesis. We provide a microstructural explanation for the observed behavior, and also look at the day-of-the-week effect for the Chilean peso and find that the different days of the week indeed have different behavior patterns. This is an important result for investment allocation and risk assessment.

Let (Xi)i∈ℕ be a sequence of independent and identically distributed random variables with values in the set ℕ0 of nonnegative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X1,…,Xn} of the first n values. We obtain necessary and sufficient conditions in terms of the tail sequence (qk)k∈ℕ0, qk=P(X1≥ k), for the gaps to vanish asymptotically as n→∞: these are ∑k=0∞qk+1/qk <∞ and limk→∞qk+1/qk=0 for convergence almost surely and convergence in probability, respectively. We further show that the length of the longest gap tends to ∞ in probability if qk+1/qk→ 1. For the family of geometric distributions, which can be regarded as the borderline case between the light-tailed and the heavy-tailed situations and which is also of particular interest in applications, we study the distribution of the length of the longest gap, using a construction based on the Sukhatme–Rényi representation of exponential order statistics to resolve the asymptotic distributional periodicities.