Wild Binary Segmentation Research Articles

Spatiotemporal analysis of precipitation and extreme indices in the Antalya Basin, Turkey

The Antalya Basin is characterised by high spatiotemporal variability of precipitation. Despite the basin’s importance for sustainable water use and its specific place in socio-economy of Turkey, the spatiotemporal patterns of precipitation are not thoroughly studied. This study aims to improve the understanding of spatiotemporal variability of precipitation and extreme precipitation indices (i.e. annual maximum 1-day and 5-day precipitation, maximum number of consecutive dry and wet days) in the basin for the period 1970–2017. To this end, trend detection methods—Mann-Kendall, modified Mann-Kendall, and Sen’s slope estimation methods—were employed with change-point detection methods—Pettitt, Buishand, Standard Normal Homogeneity, Pruned Exact Linear Time, and Wild Binary Segmentation. Further, continuous wavelet analysis was used to analyse the multi-scale resolution features of precipitation. Our results suggested three basin-wide distinct periods with the specific spatiotemporal distribution of precipitation and extreme indices among the sub-periods. The characteristics of the variability of precipitation and extreme indices for the sub-periods were discussed. The outcomes from this study could be useful to decision makers for sustainable water management and mitigate unfavourable impacts of flood and drought threats in one of the most vulnerable and sensitive basins to the impacts of climate change of the country.

Manufacturing Process Monitoring With Nonparametric Change-Point Detection in Automotive Industry

Automatic sensing devices and computer systems have been widely adopted by the automotive manufacturing industry, which are capable to record machine status and process parameters nonstop. While a manufacturing process always has natural variations, it is crucial to detect significant changes to the process for quality control, as such changes may be the early signs of machine faults. This motivates our study on change-point detection methods for automotive manufacturing. We aim at developing a systematic approach for detecting process changes retrospectively in complex, nonstationary data. The proposed approach consists of nonparametric change-point detection, alarm generation based on change-point estimations, and performance evaluation against historical maintenance records. For change-point detection, three nonparametric methods are suggested—least absolute shrinkage and selection operator (LASSO), thresholded LASSO, and wild binary segmentation (WBS). Multiple decision rules are proposed to determine how to generate alarms from change-point estimations. Numerical studies are conducted to demonstrate the performance of the proposed systematic approach. The different change-point detection methods and different decision rules are evaluated and compared, with scenarios for choosing one set of change-point detection method and decision rule over another combination identified. It is shown that LASSO and thresholded-LASSO outperform WBS when the shift size is small, but WBS produces a smaller false alarm rate and handles the clustering of changes better than LASSO or thresholded LASSO. Data from an automotive manufacturing plant are used in the case study to demonstrate the proposed approach. Guidelines for implementation are also provided.

Multiple change-point detection for non-stationary time series using Wild Binary Segmentation

We propose a new technique for consistent estimation of the number and locations of the change-points in the second-order structure of a time series. The core of the segmentation procedure is the Wild Binary Segmentation method(WBS), a technique which involves a certain randomised mechanism. The advantage of WBS over the standard Binary Segmentation lies in its localisation feature, thanks to which it works in cases where the spacings between change-points are short. In addition, we do not restrict the total number of change-points a time series can have. We also ameliorate the performance of our method by combining the CUSUM statistics obtained at different scales of the wavelet periodogram, our main change-point detection statistic, which allows a rigorous estimation of the local autocovariance of a piecewise-stationary process. We provide a simulation study to examine the performance of our method for different types of scenarios. A proof of consistency is also provided. Our methodology is implemented in the R package wbsts, available from CRAN.

Trend analysis and change point techniques: a survey

Trend analysis and change point detection in a time series are frequent analysis tools. Change point detection is the identification of abrupt variation in the process behavior due to distributional or structural changes, whereas trend can be defined as estimation of gradual departure from past norms. We examine four different change point detection methods which, by virtue of current literature, appear to be the most widely used and the newest algorithms. They are Wild Binary Segmentation, E-Agglomerative algorithm for change point, Iterative Robust Detection method and Bayesian Analysis of Change Points. We measure the power and accuracy of these current methods using simulated data. We draw comparisons on the functionality and usefulness of each method. We also analyze the data in the presence of trend, using Mann–Kendall and Cox–Stuart methods together with the change point algorithms, in order to evaluate whether presence of trend affects change point or vice versa.

Wild binary segmentation for multiple change-point detection

We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard binary segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to a significant increase in computational complexity. WBS is also easy to code. We propose two stopping criteria for WBS: one based on thresholding and the other based on what we term the `strengthened Schwarz information criterion'. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance in comparison with the state of the art. The WBS methodology is implemented in the R package wbs, available on CRAN. In addition, we provide a new proof of consistency of binary segmentation with improved rates of convergence, as well as a corresponding result for WBS.