Deterministic vs stochastic trends: detection and challenges, Journal of Geophysical Research

The detection of a trend in a time series and the evaluation of its magnitude and statistical signi.cance is an important task in geophysical research. This importance is amplifed in climate change contexts, since trends are often used to characterize long-term climate variability and to quantify the magnitude and the statistical signi.cance of changes in climate time series, both at global and local scales. Recent studies have demonstrated that the stochastic behavior of a time series can change the statistical signi.cance of a trend, especially if the time series exhibits long range dependence. The present study examines the trends in time series of daily average temperature recorded in 26 stations in the Tuscany region (Italy). In this study a new framework for trend detection is proposed. First two parametric statistical tests, the Phillips-Perron test and the Kwiatkowski-Phillips-Schmidt-Shin test, are applied in order to test for trend-stationary and di.erence stationary behavior in the temperature time series. Then long range dependence is assessed using di.erent approaches, including wavelet analysis, heuristic methods and by .tting fractionally integrated autoregressive moving average models (ARFIMA). The trend detection results are further compared with the results obtained using non-parametric trend detection methods: Mann-Kendall, Cox-stuart and Spearman’s rho test. This study con.rms an increase in uncertainty when pronounced stochastic behaviors are present in the data. Nevertheless, for approximately one third of the analyzed records, the stochastic behavior itself cannot explain the long-term features of the time series, and a deterministic positive trend is the most likely explanation.