Potential Change Points Research Articles

Interdecadal Changes in Summertime Tropical Cyclone Precipitation over Southeast China during 1960–2009

Abstract This study examines the changes in tropical cyclone (TC) precipitation and the associated contributing factors over southeast China during 1960–2009. Climatologically, TC rainfall accounts for approximately 20%–40% of the total rainfall over southeast China during boreal summer, and the contribution can even reach 50% for some of the coastal provinces, such as Guangdong, Fujian, Zhejiang, and Hainan. The dominant mode of TC rainfall reveals a dipole pattern over southern southeast China (SSC) and eastern southeast China (ESC), and the associated principal component time series exhibits remarkable interdecadal variations, with two potential change points being identified in the late 1970s and early 1990s. These interdecadal shifts in TC rainfall are also found to be synchronous with two regime shifts in total rainfall, and they can account for more than 40% of the total rainfall anomalies over the coastal regions of southeast China. To discover the dominant factors responsible for the interdecadal variations, the overall TC rainfall anomalies are broken down into three different components (rainfall frequency, rainfall intensity, and nonlinear terms) based on a new empirical statistical approach. It is found that the interdecadal variation in TC precipitation over SSC is controlled predominantly by changes in TC rainfall intensity as well as TC rainfall frequency, while that over ESC depends mainly on the intensity and the nonlinear terms. Further examination of the TC passage frequency (TPF) suggests that the significant reduction in TPF and TC rainfall frequency over SSC during 1979–92 is associated mainly with suppressed TC genesis (negative genesis effect), while the increase in TPF and TC rainfall frequency during 1993–2009 can be attributed primarily to the enhanced passage probability (positive track effect) over SSC. Meanwhile, variations in TC rainfall intensity seem to be unrelated to the TC’s own intensity change.

Identifying Change Points in a Covariate Effect on Time-to-Event Analysis with Reduced Isotonic Regression

Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate X and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.

Deciphering behavioral changes in animal movement with a “multiple change point algorithm- classification tree” framework

The recent development of tracking tools has improved our nascent knowledge on animal movement. Because of model complexity, unrealistic a priori hypotheses and heavy computational resources, behavioral changes along an animal path are still often assessed visually. A new avenue has recently been opened with change point algorithms because tracking data can be organized as time series with potential periodic change points segregating the movement in segments of different statistical properties. So far this approach was restricted to single change point detection and we propose a straightforward analytical framework based on a recent multiple change point algorithm: the PELT algorithm, a dynamic programming pruning search method to find, within time series, the optimal combination of number and locations of change points. Data segments found by the algorithm are then sorted out with a supervised classification tree procedure to organize segments by movement classes. We apply this framework to investigate changes in variance in daily distances of a migratory bird, the Macqueen’s Bustard, Chlamydotis macqueenii, and describe its movements in three classes: staging, non-migratory and migratory movements. Using simulation experiments, we show that the algorithm is robust to identify exact behavioral shift (on average more than 80% of the time) but that positive autocorrelation when present is likely to lead to the detection of false change points (in 36% of the iterations with an average of 1.97 (se = 0.06) additional change points). A case study is provided to illustrate the biases associated with visual analysis of movement patterns compared to the reliability of our analytical framework. Technological improvement will provide new opportunities for the study of animal behavior, bringing along huge and various data sets, a growing challenge for biologists, and this straightforward and standardized framework could be an asset in the attempt to decipher animal behavior.

Trend of dissolved inorganic nitrogen at stations downstream from the Three-Gorges Dam of Yangtze River

The TRAMO/SEATS program, combined with the Hodrick–Prescott (HP) filter, was used to detect trends and potential change points in time series of dissolved inorganic nitrogen (DIN) at three stations along the Yangtze River. The trend components were extracted, and two change points were successfully detected. The components revealed that DIN has been increasing at all the stations since the 1990s, although variations exist. Changes visible before 2002 illustrate the differences in agriculture development among regions upstream from the stations. The Three-Gorges Dam (TGD), which began to impound in 2003, led to years of different trends. The DIN concentration, which had been trending upward prior to that date, began a slightly downward trend because of NH4+ depletion. Readings at the Yichang station revealed this trend most strongly; those at the Hankou station less so. The Datong station was far enough away from the TGD so that no obvious effects were seen.

On the application of new tests for structural changes on global minimum-variance portfolios

We investigate if portfolios can be improved if the classical Markowitz mean–variance portfolio theory is combined with recently proposed change point tests for dependence measures. Taking into account that the dependence structure of financial assets typically cannot be assumed to be constant over longer periods of time, we estimate the covariance matrix of the assets, which is used to construct global minimum-variance portfolios, by respecting potential change points. It is seen that a recently proposed test for changes in the whole covariance matrix is indeed partially useful whereas pairwise tests for variances and correlations are not suitable for these applications without further adjustments.

Beyond 500 ka: progress and prospects in the U-Pb chronology of speleothems

It is important to understand the relative contributions of climate change and human activities to changes in runoff to sustainably manage water resources in the arid Loess Plateau, China. In this study, Chabagou River Basin in the central arid region of the Loess Plateau was selected to investigate changes in runoff, within which a series of soil conservation measures have been implemented since the late 1950s. We applied the non-parametric Kendall test (MK) and the Bayesian change point (BCP) method to identify trends and potential change points in hydro-meteorological data sequences. The results of the MK test revealed no significantly abrupt variation has been detected in annual hydro-meteorological data sequences, while a number of potential change points were identified using the BCP method applying different posterior probabilities. We also systematically review two commonly applied quantitative methods that draw on both empirical statistics and hydrological modeling to quantify the impact of climate change, human activities and meteorological variation on mean annual runoff at spatiotemporal scales based on precipitation, evapotranspiration, runoff-precipitation coefficients, and soil water throughout the river basin. The results of this study show that climate change and normal climate variability are responsible for about 80% of the decrease in runoff, mainly due to reduced precipitation, while human activities was responsible for <20% of reductions in runoff. The results also show that soil conservation measures have influenced hydrological processes at spatiotemporal and that runoff within the Chabagou River Basin (CRB) is more sensitive to spatial distribution of soil conservation measures than meteorological factors. The relative contributions to runoff variations that derive from climate change, human activities and meteorological variation were calculated in this study, but interactions between climate change and human activities is complex, and not easy to be separated.

Trend and change-point detection for the annual stream-flow series of the Karun River at the Ahvaz hydrometric station

Karun River watershed located in southwest of Iran experiences great changes in the last decade due to hydro climatic changes, large-scale land use and land cover changes, construction of dams and agricultural and industrial development. Stream-flow series of the annual maximum, annual minimum and annual mean in Ahvaz hydrometric station as representative of the watershed have been considered. In order to determine the change points, we use the Pettitt test while the trend in the annual stream-flow series of this station is evaluated by the Mann-Kendall test. However, the Pettitt test cannot detect any change point in these series, but the Mann-Kendall test shows that there is an increasing trend. This increasing trend has no fitness with observed data in recent decade. Therefore, the potential change points were determined and consequently, these series converted to two sub-series based on the results obtained from the Pettitt test, wide variation from human activities and variation of hydro climatic conditions. We then applied the Mann-Kendall test in these two sub-series which showed significant decreasing trend in both of them. From this method, it can be concluded that the averages of the second sub-series are larger than the first one in the three annual stream-flow series. This increasing ratio is equal to 1.34, 1.16 and 1.2 for stream-flow series of annual maximum, annual minimum and annual mean respectively. These changes are similar to changes in annual rainfall time series. We can say that the sudden increase of precipitation in recent decades makes the averages of the second sub-series larger. Results showed that inspite of wide range human induced changes, stream-flow series is more affected from the watershed rainfall time series variations. In addition, significant decreasing trend in the two sub-series can be due to the following causes: the growth of population, temperature rise, construction of three dams on the Karun River, implementing the different projects for developing agricultural, and conservation from soil and water resources. Key words: Pettit test, Mann-kendall test, annual stream-flow series, Ahvaz hydrometric station.

Detection and localization of multiple rate changes in Poisson spike trains

In statistical spike train analysis, stochastic point process models usually assume stationarity, in particular that the underlying spike train shows a constant firing rate (e.g. [1]). However, such models can lead to misinterpretation of the associated tests if the assumption of rate stationarity is not met (e.g. [2]). Therefore, the analysis of nonstationary data requires that rate changes can be located as precisely as possible. However, present statistical methods focus on rejecting the null hypothesis of stationarity without explicitly locating the change point(s) (e.g. [3]). We propose a test for stationarity of a given spike train that can also be used to estimate the change points in the firing rate. Assuming a Poisson process with piecewise constant firing rate, we propose a Step-Filter-Test (SFT) which can work simultaneously in different time scales, accounting for the high variety of firing patterns in experimental spike trains. Formally, we compare the numbers N1=N1(t,h) and N2=N2(t,h) of spikes in the time intervals (t-h,t] and (h,t+h]. By varying t within a fine time lattice and simultaneously varying the interval length h, we obtain a multivariate statistic D(h,t):=(N1-N2)/√(N1+N2), for which we prove asymptotic multivariate normality under homogeneity. From this a practical, graphical device to spot changes of the firing rate is constructed. Our graphical representation of D(h,t) (Figure ​(Figure1A)1A) visualizes the changes in the firing rate. For the statistical test, a threshold K is chosen such that under homogeneity, |D(h,t)|<K holds for all investigated h and t with probability 0.95. This threshold can indicate potential change points in order to estimate the inhomogeneous rate profile (Figure ​(Figure1B).1B). The SFT is applied to a sample data set of spontaneous single unit activity recorded from the substantia nigra of anesthetized mice. In this data set, multiple rate changes are identified which agree closely with visual inspection. In contrast to approaches choosing one fixed kernel width [4], our method has advantages in the flexibility of h. Figure 1 Graphical representation of the step filter test (SFT) that detects rate changes in Poisson spike trains. A. Curves indicate values of D(h,t) as a function of time t for different window sizes h (in different colors). B. Rate histogram (grey) of the corresponding ...

Testing the structural stability of temporally dependent functional observations and application to climate projections

We develop a self-normalization (SN) based test to test the structural stability of temporally dependent functional observations. Testing for a change point in the mean of functional data has been studied in Berkes, Gabrys, Horvath and Kokoszka [4], but their test was developed under the independence assumption. In many applications, functional observations are expected to be dependent, especially when the data is collected over time. Building on the SN-based change point test proposed in Shao and Zhang [23] for a univariate time series, we extend the SN-based test to the functional setup by testing the constant mean of the finite dimensional eigenvectors after performing functional principal component analysis. Asymptotic theories are derived under both the null and local alternatives. Through theory and extensive simulations, our SN-based test statistic proposed in the functional setting is shown to inherit some useful properties in the univariate setup: the test is asymptotically distribution free and its power is monotonic. Furthermore, we extend the SN-based test to identify potential change points in the dependence structure of functional observations. The method is then applied to central England temperature series to detect the warming trend and to gridded temperature fields generated by global climate models to test for changes in spatial bias structure over time.

Using Markov chain Monte Carlo and dynamic programming for event sequence data

Sequences of events are a common type of data in various scientific and business applications, e.g. telecommunication network management, study of web access logs, biostatistics and epidemiology. A natural approach to modelling event sequences is using time-dependent intensity functions, indicating the expected number of events per time unit. In Bayesian modelling, piecewise constant functions can be utilized to model continuous intensities, if the number of segments is a model parameter. The reversible jump Markov chain Monte Carlo (RJMCMC) methods can be exploited in the data analysis. With very large quantities, these approaches may be too slow. We study dynamic programming algorithms for finding the best fitting piecewise constant intensity function, given a number of pieces. We introduce simple heuristics for pruning the number of the potential change points of the functions. Empirical evidence from trials on real and artificial data sets is provided, showing that the developed methods yield high performance and they can be applied to very large data sets. We also compare the RJMCMC and dynamic programming approaches and show that the results correspond closely. The methods are applied to fault-alarm sequences produced by large telecommunication networks.

Fitting multiple change-point models to data

Change-point problems arise when different subsequences of a data series follow different statistical distributions – commonly of the same functional form but having different parameters. This paper develops an exact approach for finding maximum likelihood estimates of the change points and within-segment parameters when the functional form is within the general exponential family. The algorithm, a dynamic program, has execution time only linear in the number of segments and quadratic in the number of potential change points. The details are worked out for the normal, gamma, Poisson and binomial distributions.

Changes of Variance in First-Order Autoregressive Time Series Models-With an Application

SUMMARY A two-stage method is presented for detecting step changes of variance in first-order autoregressive time series models. Potential change points are initially located using a moving-block procedure. Given initial change points, an iterative likelihood argument is used to develop estimators of the change points, variances and autoregressive parameters. The efficacy of the method is examined with computer simulation experiments, and a numerical example using stock market data is discussed.