‘Tipping points’ in the climate system are characterised by a nonlinear response to gradual forcing, and may have severe and wide-ranging impacts. One of the best ways to identify and potentially predict threshold behaviour in the climate system is through analysis of palaeoclimate records. It has been suggested that early warning signals occur on the approach to a tipping point, generated from characteristic fluctuations in a time series as a system loses stability. Although early warning signals have been found in climate models and high-resolution marine and ice core palaeodata, studies from terrestrial records are lacking. In this study, a number of Pleistocene terrestrial records were selected to represent a range of regions strongly influenced by different climate modes which are thought to be capable of displaying threshold behaviour. These records included lake sediments from the North Atlantic, tree-rings from the South Pacific, a Chinese speleothem and were complemented by a new Greenland ice core chronology. Recently developed methods to detect signals of ‘critical slowing down’, ‘flickering’, and stability changes on the approach to a tipping point were utilised. Specific methodological issues arising from analysing palaeoclimate data were also investigated using a simple bifurcation model. A number of key criteria were found to be necessary for the reliable identification of early warning signals in palaeoclimate records, most crucially, the need for a low-noise record of sufficient data length, resolution and accuracy. Analysis of a Chinese speleothem identified the East Asian Summer Monsoon as an important climate ‘tipping element’, which may display a cascade of impacts. However, in some cases where early warning signals may fail, a deeper understanding of the underlying system dynamics is required to inform the development of more robust system-specific indicators. This was exemplified by the analysis of an abrupt, centennial-duration shutdown recorded during the Younger Dryas Chronozone in New Zealand, which demonstrated no slowing down, consistent with a freshwater pulse into the Southern Ocean. This study demonstrates that time series precursors from palaeoclimate archives provide a means of useful forewarning of many potential climate tipping points.

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In this thesis we empirically examine whether the Turkish stock market is driven by rational bubbles over the period between March 1990 and February 2012. The bubble periods are estimated using a recently developed right-tailed unit root test, the generalized sup augmented Dickey-Fuller test of Phillips, Shi and Yu (2011a). Applying their bubble detection and location strategies to weekly price dividend ratio series, we find strong evidence for the existence of rational bubbles in the Turkish stock market benchmark indices as well as sector indices. Our located bubble periods may give early warning signals of the subsequent Turkish financial crisis.

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