Print Email Facebook Twitter Capturing the uncertainty about a sudden change in the properties of time series with confidence curves Title Capturing the uncertainty about a sudden change in the properties of time series with confidence curves Author Zhou, C. (TU Delft Water Resources) van Nooijen, R.R.P. (TU Delft Water Resources) Kolechkina, A.G. (TU Delft Team Bart De Schutter) Date 2023 Abstract The representation of uncertainty in results is an important aspect of statistical techniques in hydrology and climatology. Hypothesis tests and point estimates are not well suited for this purpose. Other statistical tools, such as confidence curves, are better suited to represent uncertainty. Therefore three parametric methods to construct confidence curves for the location of a sudden change in the properties of a time series, a change point (CP), are analyzed for three distributions: log-normal, gamma, and Gumbel. Two types of change are considered: a change in the mean and a change in the standard deviation. A question that confidence curves do not answer is how likely the null hypothesis of ‘no change’ is. A possible statistic to help answer this question, denoted by Un, is introduced and analyzed. It is compared to the statistic that underlies the Pettitt test. All methods perform well in terms of coverage and confidence set size. One method is based on the profile likelihood for a CP, the other two, first defined in this article, on the pseudolikelihood for a CP. The main advantage of the pseudolikelihood over the profile likelihood lies in the much lower computational cost. The confidence curves generated by the three methods are very similar. In a limited test on time series of measurements found in the literature, the methods gave results that largely matched those reported elsewhere. Some results are also given for an order one autoregressive series with a lognormal marginal distribution. Subject Change point detectionConfidence curvesL-momentsLikelihoodMethod of momentsPseudolikelihoodStructural breakUncertainty To reference this document use: http://resolver.tudelft.nl/uuid:bf4b667a-7910-41d7-82be-6277ba76a408 DOI https://doi.org/10.1016/j.jhydrol.2023.129092 ISSN 0022-1694 Source Journal of Hydrology, 617 Part of collection Institutional Repository Document type journal article Rights © 2023 C. Zhou, R.R.P. van Nooijen, A.G. Kolechkina Files PDF 1_s2.0_S0022169423000343_main.pdf 1.52 MB Close viewer /islandora/object/uuid:bf4b667a-7910-41d7-82be-6277ba76a408/datastream/OBJ/view