We are discussing changepoint detection in tropospheric parameter time series that occurs in a numerical weather reanalysis model. Our approach applies a statistical method that is based on the maximum value of two sample t-statistics. We use critical values calculated by applying an asymptotic distribution. We also apply an asymptotic distribution to finding approximate critical values for the changepoint position. Experiments on “test” and “real” data illustrate the assumed accuracy and efficiency of our method. The method is assessed by its application to our series after adding synthetic shifts. A total of more than 3,000 original profiles are then analysed within the time-span of the years 1990-2015. The analysis shows that at least one changepoint is present in more than 9% of the studied original time series. The uncertainty of estimated times achieved tens of days for shifts larger than 9 mm, but it was increased up to hundreds of days in the case of smaller synthetic shifts. Discussed statistical method has potential for suspected change point detection in time series with higher time resolution.
A procedure for testing occurrance of a transient change in mean of a sequence is suggested where inside an epidemic interval the mean is a linear function of time points. Asymptotic behavior of considered trimmed maximum-type test statistics is presented. Approximate critical values are obtained using an approximation of exceedance probabilities over a high level by Gaussian fields with a locally stationary structure.
The paper by Jarušková and Hanek (2006) advocated application of the peaks over threshold method (POT method) for estimating the probability that a precipitation or discharges series exceeds a chosen high level. If daily precipitation amounts or average discharges are obtained at several stations one might be interested in estimating the probability that in the same time all variables of interest, e.g. precipitation amounts measured at several stations, exceed some chosen high levels. The paper explains how the method based on the point process approach may be used to get good estimates of such probabilities. Moreover, it presents some useful parametric models that were successfully applied by the author to some precipitation and discharges series of northern Moravia. and Článek navazuje na práci Jarušková, Hanek (2006), kde autoři doporučovali používání metody špiček nad prahem k odhadu pravděpodobností, s jakou srážková nebo průtoková řada překročí danou vysokou úroveň. V případě, že se denní srážková či průtoková řada měří ve více stanicích, může nás zajímat, s jakou pravděpodobností současně (to znamená ve stejný den) všechny studované řady, to je například srážkové řady měřené v několika stanicích, překročí nějaké předem stanovené vysoké úrovně. Článek vysvětluje, jak lze k odhadu takových pravděpodobností použít metodu založenou na bodovém procesu. Zároveň uvádí některé parametrické modely, které byly úspěšně použity autorkou článku pro odhady pravděpodobností překročení pro srážkové a průtokové řady na severní Moravě.
The peaks over threshold method (POT method) is an alternative to the block-maxima method for estimating return levels (these are the levels that are exceeded by a daily precipitation, resp. by a daily average discharge, only with a given small probability; in statistical language they are called high quantiles) when the studied series are not long enough. The paper compares both methods for precipitation and discharges series of Northern Moravia. It is shown how to overcome problems in the POT method caused by autocorrelation and seasonality. and Metoda špiček nad prahem může sloužit při odhadování vysokých kvantilů (to znamená takových hodnot, že je denní úhrnná srážka, respektive denní průměrný průtok, překročí jen s malou předem danou pravděpodobností). Jedná se o alternativu k metodě blokových maxim, a to zvláště tam, kde studované řady nejsou příliš dlouhé. Článek porovnává výsledky obou metod na příkladech srážkových a průtokových dat ze severní Moravy. Ukazuje dále, jak lze v metodě POT překonat problémy spojené s autokorelací a sezónností řad.
The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests for a detection of a change in an intensity of the Poisson process are described and illustrated by an example. We cover both the case when the time of the change is assumed to be known or unknown.