Algorithm for segmentation of multimodally distributed time series in accordance with their modes

Trends in temperature series are the main cause of climate change. Because solar energy directs hydro-meteorological events and increasing variations in this resource change the balance between events such as evaporation, wind, and rainfall. There are many methods for calculating trends in a time series such as Mann-Kendall, Sen's slope estimator, Spearman's rho, linear regression and the new Sen innovative trend analysis (ITA). In addition, Mann-Kendall's variant, the sequential Mann Kendall, has been developed to identify trend change points; however, it is sensitive to related data as specified by some researchers. Şen_ITA is a new trend detection method and does not require independent and normally distributed time series, but has never been used to detect trend change points. In the literature, multiple, half-time and multi-durations ITA methods are used to calculate partial trends in a time series without identifying trend change points. In this study, trend change points are detected using the Şen_ITA method and named ITA_TCP. This approach may allow researchers to identify trend change points in a time series. Diyarbakır (Turkey) is selected as a study area, and ITA_TCP has detected trends and trends change points in monthly average temperatures. Although ITA detects only a significant upward trend in August, given the 95% statistical significance level, ITA_TCP shows three upward trends in June, July and August, and a decreasing trend in September. Critical trend slope values are obtained using the bootstrap method, which does not require the normal distribution assumption.

We study the fundamental k-nearest neighbor (kNN) search problem on distributed time series. A server has constantly received various reference time series Q of length X and seeks the exact kNN over a collection of time series distributed across a set of M local sites. When X and M are large, and when the amount of query increases, simply sending each Q to all M sites incurs high communication bandwidth costs, which we would like to avoid. Prior work has presented a communication-efficient kNN algorithm for the Euclidean distance similarity measure. In this paper, we present the first communication-efficient kNN algorithm for the dynamic time warping (DTW) similarity measure, which is generally believed a better measure for time series. To handle the complexities of DTW, we design a new multi-resolution structure for the reference time series, and multi-resolution lower bounds that can effectively prune the search space. We present a new protocol between the server and the local sites that leverages multi-resolution pruning for communication efficiency and cascading lower bounds for computational efficiency. Empirical studies on both real-world and synthetic data sets show that our method reduces communication bandwidth by up to 92%.

In this paper evaluates the effects in the gasoline prices after the Brazilian downstream oil chain liberation, in late 1990s. That stage meant that the Brazilian govern, that no longer setting the maximum and minimum values of all fuels. For this purpose, the gasoline type C prices were collected from fifteen relevant cities in five economic regions of Brazil, between the years 2005 and 2014. The sequences of computational techniques were applied on these datasets. The stationary and linearity for variation prices time series were analyzed in all cities and, also, the correlations among all cities in order to recognize the times series patterns. Furthermore, the Cumulative Sum control (CUMSUM) chart was used to detect smaller parameter shifts on the distribution time series. Our results reveled distinct patterns for middle of 2005 and the middle of 2006, and also for the first months of 2011 and the middle of 2012. Reinforcing the idea of the Brazilian retail and distribution are governed strongly by exogenous factors. This makes a conventional analysis difficult to be used. Once, the Brazilian downstream fuel chain suggests to be a complexity system.

Inhomogeneous Dependency Modelling with Time Varying Copulae

Characterization of annual soil moisture response pattern on a hillslope in Bongsunsa Watershed, South Korea

A Novel Multi-resolution Representation for Streaming Time Series

Time series analysis is an important issue in the earth science-related engineering applications such as hydrology, meteorology and environmetrics. Inconsistency and nonhomogeneity that might arise in a time series yield segments with different statistical characteristics. In this study, an algorithm based on the first order statistical moment (average) of a time series is developed and applied on five time series with length ranging from 84 items to nearly 1,300. Comparison to the existing segmentation algorithms proves the applicability and usefulness of the proposed algorithm in long hydrometeorological and geophysical time series analysis.

Multivariate time-series data are gaining popularity in various urban applications, such as emergency management, public health, etc. Segmentation algorithms mostly focus on identifying discrete events with changing phases in such data. For example, consider a power outage scenario during a hurricane. Each time-series can represent the number of power failures in a county for a time period. Segments in such time-series are found in terms of different phases, such as, when a hurricane starts, counties face severe damage, and hurricane ends. Disaster management domain experts typically want to identify the most affected counties (time-series of interests) during these phases. These can be effective for retrospective analysis and decision-making for resource allocation to those regions to lessen the damage. However, getting these actionable counties directly (either by simple visualization or looking into the segmentation algorithm) is typically hard. Hence we introduce and formalize a novel problem RaTSS (Rationalization for time-series segmentation) that aims to find such time-series (rationalizations), which are actionable for the segmentation. We also propose an algorithm Find-RaTSS to find them for any black-box segmentation. We show Find-RaTSS outperforms non-trivial baselines on generalized synthetic and real data, also provides actionable insights in multiple urban domains, especially disasters and public health.

The normal operation of a device can be characterized in different temporal states. To identify these states, we introduce a segmentation algorithm called Gecko that can determine a reasonable number of segments using our proposed L method. We then use the RIPPER classification algorithm to describe these states in logical rules. Finally, transitional logic between the states is added to create a finite state automaton. Our empirical results, on data obtained from the NASA shuttle program, indicate that the Gecko segmentation algorithm is comparable to a human expert in identifying states, and our L method performs better than the existing permutation tests method when determining the number of segments to return in segmentation algorithms. Empirical results have also shown that our overall system can track normal behavior and detect anomalies.

The increasing reliance on satellite-based air quality monitoring is hindered by challenges related to data integration, accessibility, and the technical demands of geospatial processing. This study presents the development of an interactive, publicly accessible tool built on the Google Earth Engine platform that facilitates spatial and temporal analysis of air pollution using satellite and reanalysis data without requiring any coding. The tool standardizes data from Sentinel-5P (Tropospheric Monitoring Instrument, TROPOMI), GEOS-CF, and MODIS at a spatial 1 km resolution, with integrated quality filtering and customizable temporal aggregation. Users can generate distribution raster images, histograms, and time series, with export options in GeoTIFF and CSV formats. The tool’s capabilities were demonstrated through case studies focusing on the detection of increasing carbon monoxide concentrations during large-scale wildfires in Latakia, Syria, and increased PM₂.₅ levels following military operations near the Natanz nuclear site in Iran. These applications highlight the tool’s effectiveness in detecting both long-term and abrupt pollution events in data-poor regions. Compared to platforms such as NASA Giovanni or TROPOMI Viewer, the developed tool offers enhanced interactivity, data control, and multi-source integration within a single environment. By simplifying the barrier to access to environmental and health analyses, this tool provides an effective alternative for researchers, particularly in developing countries, and contributes to ongoing efforts to make geospatial air quality information accessible to all.

Considering the self-adaptive segmentation of time series in interval prediction of remaining useful life for lithium-ion battery

Stock time series segmentation is one of the fundamental components in stock time series data mining. And the segmentation is often used for the trend analysis. In this paper, a new stock time series segmentation algorithm is proposed based on PIP(Perceptually Important Point) approach. This proposed segmentation method contributes to containing both the important data points and the primitive trends like uptrend and downtrend, while most of the current algorithms only contain one aspect of that. The proposed segmentation algorithm is proved to be more efficient and effective in reserving the trends and less complexity than those combined split-and- merge piecewise linear approximation segmentation algorithms.

Joint assessment of temporal segmentation, time unit and detection algorithms in syndromic surveillance

The ratio of record highs to record lows is examined with respect to extent of time series for monthly mean temperatures within the continental United States for 1900–2006. In counting the number of records that occur in a single year, the authors find a ratio greater than unity in 2006, increasing nearly monotonically as the time series increases in length via a variable first year over 1900–76. For example, in 2006, the ratio of record highs to record lows ≈ 13:1 with 1950 as the first year and ≈ 25:1 with 1900 as the first year; both ratios are an order of magnitude greater than 3σfor stationary simulations. This indicates a warming trend. It is also found that records are more sensitive to trends in time series of monthly averages than in time series of corresponding daily values. When the last year (1920–2006, starting in 1900) is varied, it is found that the ratio of record highs to record lows is strongly correlated with the ensemble mean temperature. Correlation coefficients are 0.76 and 0.82 for 1900–2006 and 1950–2006, respectively; 3σ= 0.3 for pairs of uncorrelated stationary time series. Similar values are found for globally distributed time series: 0.87 and 0.92 for 1900–2006 and 1950–2006, respectively. The ratios evolve differently, however: global ratios increase throughout (1920–2006) whereas continental U.S. ratios decrease from about 1940 to 1970. Last, the geographical and seasonal distributions of trends are considered by summing records over time rather than ensemble. In the continental United States, the greatest excess of record highs occurs in February (≈2:1) and the greatest excess of record lows occurs in October (≈2:3). In addition, ratios are pronounced in certain regions: in February in the Midwest the ratio ≈ 5:2, and in October in the Southeast the ratio ≈ 1:2.

The discovery of useful patterns embodied in a time series is of fundamental relevance in many real applications. Repetitive structures and common type of segments can also provide very useful information of patterns in financial time series. In this paper, we introduce a time series segmentation and characterization methodology combining a hybrid genetic algorithm and a clustering technique to automatically group common patterns from this kind of financial time series and address the problem of identifying stock market prices trends. This hybrid genetic algorithm includes a local search method aimed to improve the quality of the final solution. The local search algorithm is based on maximizing a likelihood ratio, assuming normality for the series and the subseries in which the original one is segmented. To do so, we select two stock market index time series: IBEX35 Spanish index (closing prices) and a weighted average time series of the IBEX35 (Spanish), BEL20 (Belgian), CAC40 (French) and DAX (German) indexes. These are processed to obtain segments that are mapped into a five dimensional space composed of five statistical measures, with the purpose of grouping them according to their statistical properties. Experimental results show that it is possible to discover homogeneous patterns in both time series.