Effect of the uncertainty of autocorrelation estimation on trend analysis

Abstract

Autocorrelation is ubiquitous in real-life time series. For trend analysis, positive autocorrelation mainly increases the statistical uncertainty of the detected trend. The theoretical framework has been established to quantify how the autocorrelation can impact trend analysis if its characteristic is known precisely. However, if the autocorrelation is also uncertain like that estimated in real-life data, then the consequences are yet unclear. The situation is further complicated by the concurrence of both short- and long-range correlation (SLRC), e.g., in air temperature. In this study, we use an appropriate minimal model with one short-range autoregressive parameter and one long-range fractional parameter to account for such SLRC, and then accordingly propose a framework to integrate the effect of the uncertainty of autocorrelation estimation into trend analysis, on the basis of the detrended fluctuation analysis and Akaike weights. This framework can also obtain a joint probability density function of the estimated autoregressive and fractional parameters for measuring their uncertainty, identifying their combined optimal estimates, uncovering their strong interdependence, and determining their two-dimensional confidence region. The effectiveness and applicability of the proposed framework are verified by a numerical experiment and a case study of daily air temperature anomalies at the Potsdam station. This study can provide a solid theoretical basis to underpin our understanding of the autocorrelation effect on trend analysis in theory and applications. Published by the American Physical Society 2024