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1

Identification of the structure break point for data with changing variance

Witulska Justyna, Wyłomańska Agnieszka

Mathematica Applicanda

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2022

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Vol. 50, no. 1

65--106

EN

In this paper, we discuss the problem of the structure break point detection for data with changing variance. Considering the limitations and advantages of five well-known techniques, we propose a hybrid algorithm dedicated to the considered problem. The new method enables us to detect break point, even if the data exhibit non-Gaussian characteristics and the small differences between variances in separate segments occur. The efficiency is verified for simulated data from three general classes of distributions, namely platykurtic, leptokurtic and mesokurtic classes represented here by Gaussian, Laplace, Student's t, and generalized Gaussian distributions. The simulation study is supported by real data analysis.

PL

W artykule omówiono problem detekcji punktu zmiany reżimu dla danych o zmiennej wariancji. Uwzględniając ograniczenia i zalety pięciu znanych technik, zaproponowano hybrydowe podejscie dla omawianego problemu. Nowa metoda umożliwia wykrycie punktu zmiany, nawet jeśli dane wykazują charakterystykę niegaussowską i występują niewielkie różnice pomiędzy wariancjami w poszczególnych segmentach. Skuteczność metody jest weryfikowana dla danych symulowanych pochodzących z trzech ogólnych klas rozkładów, mianowicie platykurtycznych, leptokurtycznych oraz mezokurtycznych reprezentowanych tutaj przez rozkład normalny, Laplace'a, t-Studenta oraz uogólniony rozkład normalny. Badania symulacyjne poparte są analizą danych rzeczywistych.

2

The use of hybrid methods for change points and trends detection in rainfall series of northern Algeria

Zerouali Bilel, Chettih Mohamed, Abda Zaki, Mesbah Mohamed, Djemai Mohammed

Acta Geophysica

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2020

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Vol. 68, no. 5

1443--1460

EN

The aim of this research is to assess relatively new hybrid methods for changes points and trends detection on rainfall series: Dynamic Programming Bayesian Change Point Approach (BA), Şen’s innovative trend method (ITM) and its double (D-ITM) and triple (T-ITM) version using the multi-scale analysis of the discrete wavelet transform (DWT) as a coupling method. Three representatives rainfall stations of northern Algeria were analysed at annual scale during the period 1920–2011. Moreover, correlation and spectral analysis (CSA) was applied for periodicity analysis. The CSA indicates the dominance of interannual to multidecadal rainfall periodicity fuctuations (2-years, 5-years and 20-years) characterising long term structured processes. Moreover, an abrupt downward trend with signifcant probability was detected from the 1970s with a relatively wet period between the periods 1950–1970 and 2001–2011. The latter is observed in particular in the central and eastern stations, well-explained by the BA-DWT. The results showed that the comparison results from diferent modelling approaches found that the hybrid models (BA-DWT, ITM-DWT, D-ITM-DWT, T-ITM-DWT) often perform better than the conventional approach (BA, ITM, D-ITM, T-ITM), where the computation time is very reasonable. The analysis revealed that information stemming from discrete wavelet spectrums signifcantly increased the accuracy of the methods for detecting hidden change points and trends.

3

Spatio-temporal analysis of rainfall trends in Chhattisgarh State, Central India over the last 115 years

Nema M. K., Khare D., Adamowski J., Chandniha S. K.

Journal of Water and Land Development

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2018

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no. 36

117--128

EN

A quantitative and qualitative understanding of the anticipated climate-change-driven multi-scale spatio- -temporal shifts in precipitation and attendant river flows is crucial to the development of water resources management approaches capable of sustaining and even improving the ecological and socioeconomic viability of rainfed agricultural regions. A set of homogeneity tests for change point detection, non-parametric trend tests, and the Sen’s slope estimator were applied to long-term gridded rainfall records of 27 newly formed districts in Chhattisgarh State, India. Illustrating the impacts of climate change, an analysis of spatial variability, multitemporal (monthly, seasonal, annual) trends and inter-annual variations in rainfall over the last 115 years (1901– 2015 mean 1360 mm·y–1) showed an overall decline in rainfall, with 1961 being a change point year (i.e., shift from rising to declining trend) for most districts in Chhattisgarh. Spatio-temporal variations in rainfall within the state of Chhattisgarh showed a coefficient of variation of 19.77%. Strong inter-annual and seasonal variability in regional rainfall were noted. These rainfall trend analyses may help predict future climate scenarios and thereby allow planning of effective and sustainable water resources management for the region.

PL

Ilościowe i jakościowe rozpoznanie przewidywanych wielowymiarowych zmian opadów i towarzyszących im przepływów w rzekach spowodowanych zmianami klimatu jest decydujące dla rozwoju metod zarządzania zasobami wodnymi zdolnych utrzymać lub nawet usprawnić rentowność obszarów rolniczych zasilanych opadami. Zastosowano kilka testów jednorodności do wykrycia punktu zwrotnego, nieparametryczne testy trendu i estymator nachylenia Sena do analizy wieloletnich danych o opadach w 27 nowo utworzonych dystryktach stanu Chhattisgarh w Indiach. Ilustrując wpływ zmian klimatu, wyniki analizy przestrzennej zmienności, miesięcznych, sezonowych i rocznych trendów oraz zmienności między latami (1901–2015, średni opad 1360 mm·r–1) wykazały ogólne zmniejszenie ilości opadów w większości dystryktów stanu Chhattisgarh. Rok 1961 był punktem zwrotnym między rosnącym a malejącym trendem opadów. Współczynnik zmienności przestrzennej i czasowej opadów w stanie Chhattisgarh wynosił 19,77%. Zanotowano znaczną zmienność opadów między poszczególnymi latami i porami roku. Takie analizy trendów mogą być przydatne w przewidywaniu przyszłych scenariuszy klimatycznych, a w związku z tym – umożliwić wydajne i zrównoważone zarządzanie zasobami wodnymi regionu.

4

A study of Optimal Testing Resource Allocation Problem for Modular Software with Change Point

Kaur G., Aggarwal A. G., Kedia A.

Annals of Computer Science and Information Systems

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2018

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Vol. 14

77--84

EN

For evolving trustworthy software, engrossing on uncovering process of fault in software is central. Nevertheless, during testing, modifications in the testing routine, defect gravity or testing-skill maturity and working environment, there can be notable change in fault detection rate. When this sort of pattern is observed in testing time it is called change point. In this article, we inquire a resource distribution problem that optimally distributes software developing resources among modules such that the total software development cost is minimized. In this problem the effect of chief circumstantial element of change-point is considered in each module. The constraint of pulling off the desired reliability level for every individual module is also incorporated in the formulation of the problem. An algorithm based on Karush Kuhn Tucker (KKT) optimality conditions is presented to solve the resulting non-linear optimization problem. A simulated numerical illustration has been analyzed to reflect the formulation of the case and its solution by the algorithm proposed.

5

Wstępna analiza parametrów termicznych zestawu szybowego wypełnionego materiałem fazowo zmiennym

Wieprzkowicz A., Heim D.

Fizyka Budowli w Teorii i Praktyce

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2017

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T. 9, nr 1

39--44

PL

W pracy przedstawiono wyniki analiz numerycznych dynamiki cieplnej wybranych rodzajów oszklenia modyfikowanych materiałem fazowo-zmiennym (MFZ). Analizy wykonano dla dwóch zestawów danych meteorologicznych, charakterystycznych dla klimatu umiarkowanego oraz podzwrotnikowego oraz trzech orientacji przegrody względem stron świata. W zależności od lokalizacji zdefiniowano 2 rozwiązania techniczne przegrody. Zaproponowano 3 kryteria determinujące żądane temperatury przemiany fazowej MFZ wypełniającego jedną z przestrzenni międzyszybowych. Na podstawie wyników analiz numerycznych wyznaczono wymagane temperatury oraz dobrano dostępne materiały z grupy parafin. Wybrane materiały stanowią niskotemperaturowe magazyny ciepła w zakresie temperatur przemiany 18-21°C w przypadku doboru dla okresu zimowego oraz 25-31°C (35°C dla Santiago) w przypadku analiz przeprowadzonych dla lata.

EN

The paper presents results of numerical analysis of thermal dynamics of selected types of glazing modified with phase-change material (PCM). The analyzes were performed for two sets of meteorological data, typical for the moderate and subtropical climate, and the three orientations of façade. Depending on the location, two technical solutions were defined. Three criteria have been proposed to determine the most efficient phase transition temperature of PCM filling one of the window cavities. Based on the results of numerical analysis, the required temperatures were determined and materials from the paraffin group were selected. Selected materials are low temperature heat stores with a transition temperature of 18-21°C for winter season and 25-31°C (35°C for Santiago) for summer analyzes.

6

Semi-parametric modification of cumulative sum algorithms for the change-point detection of non-Gaussian sequences

Zabolotnii S. W, Warsza Z. L.

Measurement Automation Monitoring

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2015

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Vol. 61, No. 12

532--534

EN

The expansion of logarithm likelihood ratio in the stochastic series to find the sequential change-point detection of non-Gaussian sequences is used. The moment criteria of the minimum of upper limit error probabilities sum to find the expansion coefficients is applied. The proposed method is a semi-parametric type of cumulative sum (CUSUM) algorithm which needs of higher-order statistics. Results show that polynomial algorithms are more effective in comparison with similar non-parametric procedures.

7

On a random number of disorders

Szajkowski K.

Probability and Mathematical Statistics

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2011

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Vol. 31, Fasc. 1

17--45

EN

We register a random sequence which has three segments being the homogeneous Markov processes. Each segment has its own onestep transition probability law and the length of the segment is unknown and random. It means that at two random moments θ1, θ2, where 0 ≤ θ1 ≤ θ2, the source of observation is changed. In effect, the number of homogeneous segments is random. The transition probabilities of each process are known and the a priori distribution of the disorder moments is given. The former research on such a problem has been devoted to various questions concerning the distribution changes. The random number of distributional segments creates new problems in solutions with relation to analysis of the model with deterministic number of segments. Two cases are presented in detail. In the first one the objective is to stop on or between the disorder moments while in the second one our objective is to find the strategy which immediately detects the distribution changes. Both problems are reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function.