How one might miss early warning signals of critical transitions in time series data: A systematic study of two major currency pairs

Abstract

There is growing interest in the use of critical slowing down and critical fluctuations as early warning signals for critical transitions in different complex systems. However, while some studies found them effective, others found the opposite. In this paper, we investigated why this might be so, by testing three commonly used indicators: lag-1 autocorrelation, variance, and low-frequency power spectrum at anticipating critical transitions in the very-high-frequency time series data of the Australian Dollar-Japanese Yen and Swiss Franc-Japanese Yen exchange rates. Besides testing rising trends in these indicators at a strict level of confidence using the Kendall-tau test, we also required statistically significant early warning signals to be concurrent in the three indicators, which must rise to appreciable values. We then found for our data set the optimum parameters for discovering critical transitions, and showed that the set of critical transitions found is generally insensitive to variations in the parameters. Suspecting that negative results in the literature are the results of low data frequencies, we created time series with time intervals over three orders of magnitude from the raw data, and tested them for early warning signals. Early warning signals can be reliably found only if the time interval of the data is shorter than the time scale of critical transitions in our complex system of interest. Finally, we compared the set of time windows with statistically significant early warning signals with the set of time windows followed by large movements, to conclude that the early warning signals indeed provide reliable information on impending critical transitions. This reliability becomes more compelling statistically the more events we test.