Break function regression

The break is a continuous function consisting of two linear parts. It serves as a regression model for trend changes in time series. A typical application field of such a model is climatology. We introduce break-model fitting by combining a weighted least-squares criterion with a brute-force search. We explain how to determine error bars and confidence intervals for the break model parameters by means of autoregressive bootstrap resampling. Our approach takes into account the statistical properties of real-world climatological problems: non-Gaussian distributional shape, serial dependence, uneven time spacing and timescale uncertainties. A Monte Carlo experiment shows the excellent coverage performance of bootstrap bias-corrected and accelerated confidence intervals for data sizes above 100 or 200. An application quantifies trend changes in modelled Arctic river runoff during the interval from 1936 to 2001.