scholarly journals Power of parametric and non-parametric tests for trend detection in annual maximum series

2019 ◽  
Author(s):  
Vincenzo Totaro ◽  
Andrea Gioia ◽  
Vito Iacobellis
Keyword(s):  
Time Series ◽  
Model Selection ◽  
Probability Distribution ◽  
Generalized Extreme Value Distribution ◽  
Change Points ◽  
Trend Detection ◽  
Correct Selection ◽  
Stationary Probability ◽  
Parametric Methods ◽  
Non Parametric

Abstract. The need of fitting time series characterized by the presence of trend or change points has generated in latest years an increased interest in the investigation of non-stationary probability distributions. Considering that the available hydrological time series can be recognized as the observable part of a stochastic process with a definite probability distribution, two main topics can be tackled in this context: the first one is related to the definition of an objective criterion for choosing whether the stationary hypothesis can be adopted, while the second one regards the effects of non-stationarity on the estimation of distribution parameters and quantiles for assigned return period and flood risk evaluation. Although the time series trend or change points can be recognized using classical tests available in literature (e.g. Mann–Kendal or CUSUM test), for design purpose it is still required the correct selection of the stationary or non-stationary probability distribution. By this light, the focus is shifted toward model selection criteria which implies the use of parametric methods with all related issues on parameters estimation. The aim of this study is to compare the performance of parametric and non-parametric methods for trend detection analysing their power and focusing on the use of traditional model selection tools (e.g. Akaike Information Criterion and Likelihood Ratio test) within this context. Power and efficiency of parameter estimation, including the trend coefficient, were investigated through Monte Carlo simulations using Generalized Extreme Value distribution as parent with selected parameter sets.

scholarly journals Numerical investigation on the power of parametric and nonparametric tests for trend detection in annual maximum series

2020 ◽  
Vol 24 (1) ◽  
pp. 473-488 ◽  
Author(s):  
Vincenzo Totaro ◽  
Andrea Gioia ◽  
Vito Iacobellis
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Model Selection ◽  
Probability Distribution ◽  
Nonparametric Tests ◽  
Generalized Extreme Value Distribution ◽  
Change Points ◽  
Trend Detection ◽  
Correct Selection ◽  
Ratio Test

Abstract. The need to fit time series characterized by the presence of a trend or change points has generated increased interest in the investigation of nonstationary probability distributions in recent years. Considering that the available hydrological time series can be recognized as the observable part of a stochastic process with a definite probability distribution, two main topics can be tackled in this context: the first is related to the definition of an objective criterion for choosing whether the stationary hypothesis can be adopted, whereas the second regards the effects of nonstationarity on the estimation of distribution parameters and quantiles for an assigned return period and flood risk evaluation. Although the time series trend or change points are usually detected using nonparametric tests available in the literature (e.g., Mann–Kendall or CUSUM test), the correct selection of the stationary or nonstationary probability distribution is still required for design purposes. In this light, the focus is shifted toward model selection criteria; this implies the use of parametric methods, including all of the issues related to parameter estimation. The aim of this study is to compare the performance of parametric and nonparametric methods for trend detection, analyzing their power and focusing on the use of traditional model selection tools (e.g., the Akaike information criterion and the likelihood ratio test) within this context. The power and efficiency of parameter estimation, including the trend coefficient, were investigated via Monte Carlo simulations using the generalized extreme value distribution as the parent with selected parameter sets.

scholarly journals Can innovative trend analysis identify trend change points?

2020 ◽  
Vol 1 (3) ◽  
pp. 6-15
Author(s):  
Sadık Alashan
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Statistical Significance ◽  
Bootstrap Method ◽  
Change Points ◽  
Trend Detection ◽  
Significance Level ◽  
Related Data ◽  
Innovative Trend Analysis ◽  
June July

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.

scholarly journals Can innovative trend analysis identify trend change points?

2020 ◽  
Vol 1 (3) ◽  
pp. 6-15
Author(s):  
Sadık Alashan
Keyword(s):  
Time Series ◽  
Trend Analysis ◽  
Statistical Significance ◽  
Bootstrap Method ◽  
Change Points ◽  
Trend Detection ◽  
Significance Level ◽  
Related Data ◽  
Innovative Trend Analysis ◽  
June July

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.

scholarly journals Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Non-parametric Methods

2021 ◽  
Author(s):  
Hans H. Diebner ◽  
Nina Timmesfeld
Keyword(s):  
Time Series ◽  
Basic Reproduction Number ◽  
Delay Time ◽  
Reproduction Number ◽  
Intermediate Step ◽  
Parametric Methods ◽  
Temporal Behaviour ◽  
Time Courses ◽  
The Basic Reproduction Number ◽  
Non Parametric

Based on comprehensible non-parametric methods, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented. Where appropriate, the estimates for Germany are compared with the results for seven other countries (FR, IT, US, UK, ES, CH, BR) to get an idea of the breadth of applicability and a relational understanding. Thereby, only prevalence data of daily reported new counts of diagnosed cases and fatalities provided by the Johns Hopkins University are used. Drawing on uncertain a priori knowledge is avoided. Specifically, we present estimates resulting from delay-time correlations for the duration from diagnosis to death being 13 days for Germany and Switzerland. The delay-time correlation applied to time series from other countries exhibit less pronounced peaks suggesting high variabilities for the corresponding time-to-death durations. With respect to the German data, the two time series of new cases and fatalities exhibit a strong coherence within the frequency range of interest, which backs our findings. Furthermore, based on the knowledge of this time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated having superiority compared to the commonly published case-fatality rate. The temporal median of the instantaneous fatality-case ratio with proper delay of 13-days between cases and deaths for Germany turns out to be 0.02. Time courses of asymptotic fatality-case ratios are presented for other countries which substantially differ during the first half of the pandemic, however, converge to a narrow range with standard deviation 0.57% and mean 2.4%. Additionally, the time courses of instantaneous fatality-case ratios with optimal delay for the 8 exemplarily chosen countries are calculated and compared by means of the temporal medians. Similarly to the asymptotic fatality-case ratios, the differences are much smaller than expected from mass media reports. The basic reproduction number, R0, for Germany is estimated to be between 2.4 and 3.4. The uncertainty stems from uncertain knowledge of the generation time. A delay autocorrelation shows resonances at about 4 days and 7 days, where the latter resonance is at least partially attributable to the sampling process with weekly periodicity. The calculation of the basic reproduction number is based on an evaluation of cumulative numbers of cases yielding time-dependent doubling times as an intermediate step. This allows to infer to the reproduction number during the early phase of onset of the epidemic. In a second approach, the instantaneous reproduction number is derived from the incident (counts of new) cases and allows, in contrast to the first version, to infer to the temporal behaviour of the reproduction number during the later epidemic course. The time course of the reproduction number is compared to an alternative control measure given by the per capita growth, which largely confirms the conclusions drawn from the reproduction number. To conclude, by avoiding complicated parametric models we provide insights into basic features of the COVID-19 epidemic in an utmost transparent and comprehensible way. The perhaps most striking insight is that the fatality-case ratios do not differ between countries as much as previously suspected.

scholarly journals Change points in space-time, methodology and applications

2019 ◽  
pp. 17-28
Author(s):  
Lucila Muñiz –Merino ◽  
Bulmaro Juárez-Hernandez ◽  
Hugo Adan Cruz-Suares
Keyword(s):  
Change Point ◽  
Space Time ◽  
Change Points ◽  
Parametric Methods ◽  
Temporal Space ◽  
Non Parametric

In this work, we review publications which analyze, develop and apply concepts of change points, in general, the formulation of the problem of the change point, and different problems, including some of its applications are presented. Applications include temporal, spatial and temporal-space change points, parametric and non-parametric methods are used.

scholarly journals High-order Vector Markov Chain with Partial Connections in Data Analysis

2017 ◽  
Vol 46 (3-4) ◽  
pp. 37-45 ◽  
Author(s):  
Yuriy Kharin ◽  
Michail Maltsew
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
Markov Chain ◽  
Data Analysis ◽  
Probability Distribution ◽  
Discrete Time ◽  
Model Parameters ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Conditional Probability Distribution

A new mathematical model for discrete time series is proposed: homogenous vector Markov chain of the order s with partial connections. Conditional probability distribution for this model is determined only by a few components of previous vector states. Probabilistic properties of the model are given: ergodicity conditions and conditions under which the stationary probability distribution is uniform. Consistent statistical estimators for model parameters are constructed.

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