Using GARCH Models to Detect Forthcoming Transitions in Tree Growth

In numerous ecological systems, forthcoming critical transitions can be identified using a variety of methods for deriving early warning indicators. Several methods focus on characteristics of time-series related to system behaviour or properties, including changes in time-series variability. One such method is conditional heteroskedasticity (CH). CH defines a time series as having a non-constant variability, that is also dependent on the variability at previous time-steps, where increases in variability indicate that the system under study is nearing a critical transition. Here, we apply this concept to time series of radial growth, measured as tree-ring widths: a general autoregressive conditional heteroskedasticity (GARCH) model is used to produce a CH time-series from detrended tree-ring data. By analysing the variability trends within this time series, conclusions can be made relating to the system’s proximity to transition. Whilst this form of analysis is not a novel concept in the field of ecology, such a thorough examination of the models’ ability to detect change in the variability of tree-ring data is yet to be carried out. We propose the application of a dual-model approach, using both GARCH and VS-Lite models, with an aim of determining the efficacy of such a strategy to detect not only changes in tree-growth stability, but more specifically changes induced by climate stressors. This approach has the potential to forecast impending critical transitions in tree-growth behaviour, possible fluctuations in the rate of mortality, and quantify the influence of climate on growth stability at both the tree and site-level.