Estimation of linear trend onset in time series

We propose a method to detect the onset of linear trend in a time series and estimate the change point T from the profile of a linear trend test statistic, computed on consecutive overlapping time windows along the time series. We compare our method to two standard methods for trend change detection and evaluate them with Monte Carlo simulations for different time series lengths, autocorrelation strengths, trend slopes and distribution of residuals. The proposed method turns out to estimate T better for small and correlated time series. The methods were also applied to global temperature records suggesting different turning points.