Some Problems with Application of Change-Point Detection Methods to Environmental Data

Abstract

This paper summarizes the author's experience in researching methods of discovering a change in the behaviour of meteorological and hydrological series. Basic statistical tests applying ‘maximum’ type statistics to detect a sudden or gradual change in location are given. The author stresses that the characteristic properties of the meteorological and hydrological data, especially the dependence between neighbouring observations, have to be considered by performing statistcal tests for change‐point detection. © 1997 John Wiley & Sons, Ltd.

Application of MCMC to change point detection

“…The sequence of average year temperatures measured in Klementinum has already been analyzed by many other statisticians, see [2], [9] or [10] among others for different approaches. It is evident that different authors used different methods.…”

Change detection in dynamic attributed networks

“…In most scientific studies, data are generated as multivariate time series. Some examples include, climate studies where time varying data are collected on multiple variables such as temperature, precipitation and water discharges (Jarušková, ) and studies on financial markets where data on asset returns are observed over time (Lavielle & Teyssiere, ). Given multivariate time series data, a change in the correlation structure may indicate a change‐point in the overall system.…”

Change Point Detection by State Space Modeling of Long-Term Air Temperature Series in Europe

“…Environmental data have three main properties that characterize their temporal evolution: seasonality, skewed distribution and dependence besides non-stationarity [27]. In this context, state space models are very flexible to accommodate these properties and the Kalman filter algorithm is very useful even in the case of non-normality, since its predictions are the best linear unbiased estimators.…”

“…In order to identify an abrupt change in the behavior of the temperature time series, a statistical test of the maximum type is applied to detect a change in the location of innovations or in the Kalman smoothers [27]. In a first stage, this type of test is developed assuming that the time c, where the change may have occurred, is known and, in a second phase, the test statistic is computed for all the possibilities of c and its maximum is determined.…”

“…When random variables X 1 , X 2 , ..., X n are not independent but form an ARMA process, then the asymptotic critical values of the test statistics considering independence have to be multiplied by 2π f (0)/γ, where γ = var(X t ) and f (•) denotes the spectral density function of the corresponding ARMA process [37]. Especially for an AR(1) sequence, the critical values should be multiplied by (1 + φ)(1 − φ) −1 1/2 where φ is the first autoregressive coefficient [27].…”