Change-point Estimation Research Articles

Estimating supply and demand elasticities of dissolving pulp, lignocellulose-based chemical derivatives and textile fibres in an emerging forest-based bioeconomy

In a growing bioeconomy, traditional forest products markets change and diversify. Fossil-based inputs in the chemical, textile, apparel and downstream industries can be replaced by lignocellulose-based products such as dissolving pulp, cellulose-based chemical derivatives and textile fibres. When looking ahead, these previous niche products are likely to gain in economic importance. So far, little attention has been paid to the characteristics of macroeconomic relations of emerging lignocellulose-based materials on macroeconomic level. Key economic parameters for such materials are not available neither at regional nor at global level. This work aims to contribute to a better understanding of the market behavior of emerging forest products that are not yet covered by forest products market analysis. Therefore, this paper investigates how lignocellulose-based products respond to changes of main economic drivers and compute global market elasticities for dissolving pulp, cellulose-based chemical derivatives and textile fibres. To conduct our evaluation, we first test historical input data for non-constancy in time series due to structural changes using change-point estimator (MOSUM test). We subsequently carry out a global econometric analysis of demand and supply elasticities with income (GDP) and real import and export prices as explanatory variables. By doing so, we deliver key information for the adaptation of forest-product market analysis and modelling to an upcoming bioeconomy. The results show several structural changes especially in price data between 1992 and 2015, thus supporting the use of time series cuts to divide the time line from 1992 to 2015 into three different sub-periods. Elasticities are subsequently estimated for each of the sub-periods. The results from this econometric analysis provide import demand and export supply elasticities of dissolving pulp, cellulose chemical derivatives and cellulose textile fibres. In addition, we present elasticity estimation for the apparent consumption of dissolving pulp. Our findings outline the significant relationship between both export supply and import demand volumes and relative changes in prices and income. Across time periods, elasticities of cellulose-based derivatives and textile fibres do not show a clear trend towards more elastic or inelastic coefficients. However, the price elasticities of dissolving pulp fluctuate strongly from inelastic to highly elastic over time. Elasticity estimates of export supply indicate that it is sensitive to international competitiveness which in turn is governed by international demand. Finally, we statistically show that the estimated price and income elasticities of import demand can be analogously interpreted as the demand elasticity of apparent consumption. This is of great importance for economic equilibrium models, such as GFPM or EFI-GTM, in order to simulate and analyze forest sector developments and scenarios.

Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

In this article, we study the problem of multiple change-point detection for a univariate sequence under the epidemic setting, where the behavior of the sequence alternates between a common normal state and different epidemic states. This is a nontrivial generalization of the classical (single) epidemic change-point testing problem. To explicitly incorporate the alternating structure of the problem, we propose a novel model selection based approach for simultaneous inference on both change-points and alternating states. Using the same spirit as profile likelihood, we develop a two-stage alternating pruned dynamic programming algorithm, which conducts efficient and exact optimization of the model selection criteria and has as the worst case computational cost. As demonstrated by extensive numerical experiments, compared to classical general-purpose multiple change-point detection procedures, the proposed method improves accuracy for both change-point estimation and model parameter estimation. We further show promising applications of the proposed algorithm to multiple testing with locally clustered signals, and demonstrate its advantages over existing methods in large scale multiple testing, in DNA copy number variation detection, and in oceanographic study. Supplementary material for this article is available online.

Wavelet change-point estimation for the density based on biased sample

The appearance of change-points in the biased density estimation process may worsen the estimation effectiveness. To evaluate the density more accurately, we first detect the change-points by the peaks-over-threshold method and subsequently provide the estimation of the jump sizes. On the basis of change-point and their jump size estimations, we further propose the wavelet change-point density estimation and this estimation is shown to achieve the optimal convergence rate in theory. Furthermore, we present some examples that the biased density functions contain change-point(s) and implement the corresponding simulations to show that our proposed method improves the effectiveness of biased density estimation. Finally, the wavelet change-point density estimation is applied to a real-life dataset.

Linking environmental with biological data: Low sampling frequencies of chemical pollutants and nutrients in rivers reduce the reliability of model results

Linking environmental and biological data using ecological models can provide crucial knowledge about the effects of water quality parameters on freshwater ecosystems. However, a model can only be as reliable as its input data. Here, the influence of sampling frequency of temporal variable environmental input data on the reliability of model results when linked to biological data was investigated using Threshold Indicator Taxa Analysis (TITAN) and species sensitivity distributions (SSDs). Large-scale biological data from benthic macroinvertebrates and matching water quality data including four metals and four nutrients of up to 559 site-year combinations formed the initial data sets. To compare different sampling frequencies, the initial water quality data sets (n = 12 samples per year, set as reference) were subsampled (n = 10, 8, 6, 4, 2 and 1), annual mean values calculated and used as input data in the models. As expected, subsampling significantly reduced the reliability of the environmental input data across all eight substances. For TITAN, the use of environmental input data with a reduced reliability led to a considerable (1) loss of information because valid taxa were no longer identified, (2) gain of unreliable taxon-specific change points due to false positive taxa, and (3) bias in the change point estimation. In contrast, the reliability of the SSD results appeared to be much less reduced. However, closer examination of the SSD input data indicated that existing effects were masked by poor model performance. The results confirm that the sampling frequency of water quality data significantly influences the reliability of model results when linked with biological data. For studies limited to low sampling frequencies, the discussion provides recommendations on how to deal with low sampling frequencies of temporally variable water quality data when using them in TITAN, in SSDs, and in other ecological models.

Smoking during pregnancy: changes and associated risk factors in Spain, 1980-2016.

Trends for maternal smoking rates have varied substantially across industrialized countries. The objective was to describe how the prevalence of maternal smoking evolved in Spain during 1980-2016. Data came from the Spanish Collaborative Study of Congenital Malformations. Our sample consisted of 40934 mothers of newborns with no congenital defects from hospitals all across Spain. We estimated change points in trend and the mean annual change in smoking prevalence using 'joinpoint' regression. Relevant potential factors (age, country of birth, education, parity, planned pregnancy and alcohol consumption) were examined using multivariate logistic regression. Maternal smoking prevalence in 1980 and 2016 were 14.3% (95% confidence interval [CI]: 11.9-17.0) and 20.4% (95% CI: 15.9-25.8). We identified four periods with distinct trends: a sharp increase during the 80s, a plateau during the 90s, a decrease starting in 2000 and a slowdown of such decrease from 2009 on. Smoking was significantly higher among young women, Spain-born, with low education, unplanned pregnancy, and alcohol consumption. Currently in Spain maternal smoking remains very high. Tobacco consumption trend showed an increase during the 80s, a plateau during the 90s, and a reduction in the 2000s. Several sociodemographic and behavioural factors were associated to greater likelihood of smoking.

Implications of Aggregating and Smoothing Daily Production Data on Estimates of the Transition Time Between Flow Regimes in Horizontal Hydraulically Fractured Bakken Oil Wells

The level to which data are aggregated or smoothed can impact analytical and predictive modeling results. This paper discusses findings regarding such impacts on estimating change points in production flow regimes of horizontal hydraulically fractured shale oil wells producing from the middle member of the Bakken Formation. Change points that signal transitions in flow regimes are important because they subsequently affect estimates of ultimate recovery from wells producing from shale plays. Extending our earlier work, we employ two different statistical approaches, Bacon–Watts Bayesian regression and nonlinear constrained least squares regression, and a designed computational experiment to estimate the time of transition from the transient to the boundary-dominated flow regime for 14 different wells using daily production data rather than aggregated monthly data, as previously considered. The daily data were also smoothed to reduce noise. Computational experiments suggest that both statistical approaches can lead to plausible estimates of the transition point under different data aggregation or smoothing regimes, but that daily data are likely too granular to produce credible estimates. Although the expected value of transition points using smoothed daily data and monthly disaggregated data are generally comparable, the confidence intervals bounding the estimates based on smoothed daily data are generally wider. Our results not only inform the operational practices of oil producers engaged in economic evaluation of their shale resources and additional play development activities, but also the activities of petroleum research groups, government agencies, and financial organizations seeking to improve the trustworthiness of resource projections.

Maximum likelihood estimation of the change point in stationary state of auto regressive moving average (ARMA) models, using SVD-based smoothing

The change point estimation concept is usually useful in time series models. This concept helps to decrease the decision making or production costs by monitoring the stock market and production lines. It is also applied in several fields such as Financing and Quality Control. In this paper, it is assumed that the ARMA (1) model exists between the sample statistics of control chart. A maximum likelihood technique is developed to estimate the change point at which the stationary ARMA (1) model changes into a non-stationary process. For the estimation of unknown parameters after the change point, the Smoothing of Dynamic Linear Model has been used based on singular value decomposition. It is assumed that there exists a correlation between sample statistics. Simulation results show the effectiveness of the estimators proposed in this paper to estimate the change point of the stationary state in ARMA (1) model. An example is provided to illustrate the application.

Consistency of an Estimator for Change Point in Volatility of Financial Returns

A non parametric Auto-Regressive Conditional Heteroscedastic model for financial returns series is considered in which the conditional mean and volatility functions are estimated non-parametrically using Nadaraya Watson kernel. A test statistic for unknown abrupt change point in volatility which takes into consideration conditional heteroskedasticity, dependence, heterogeneity and the fourth moment of financial returns, since kurtosis is a function of the fourth moment is considered. The test is based on L2norm of the conditional variance functions of the squared residuals. A non-parametric change point estimator in volatility of financial returns is further obtained. The consistency of the estimator is shown theoretically and through simulation. An application of the estimator in change point estimation in volatility of United States Dollar/Kenya Shilling exchange rate returns data set is made. Through binary segmentation procedure, three change points in volatility of the exchange rate returns are estimated and further accounted for.

Change point estimation in regression model with response missing at random

Based on the approach of left and right kernel smoothing with unilateral kernel function, we, in this paper, define estimators of change point and jump size in nonparametric regression model with response missing at random. It is shown that the change point estimator is n-consistent and converges to the smallest maximizer of one-dimensional bilateral compound Poisson process, the jump size estimator is asymptotically normal. A simulation study is conducted to investigate the finite sample behavior for the proposed methods.

Changepoint in Error-Prone Relations

Linear relations, containing measurement errors in input and output data, are considered. Parameters of these so-called errors-in-variables models can change at some unknown moment. The aim is to test whether such an unknown change has occurred or not. For instance, detecting a change in trend for a randomly spaced time series is a special case of the investigated framework. The designed changepoint tests are shown to be consistent and involve neither nuisance parameters nor tuning constants, which makes the testing procedures effortlessly applicable. A changepoint estimator is also introduced and its consistency is proved. A boundary issue is avoided, meaning that the changepoint can be detected when being close to the extremities of the observation regime. As a theoretical basis for the developed methods, a weak invariance principle for the smallest singular value of the data matrix is provided, assuming weakly dependent and non-stationary errors. The results are presented in a simulation study, which demonstrates computational efficiency of the techniques. The completely data-driven tests are illustrated through problems coming from calibration and insurance; however, the methodology can be applied to other areas such as clinical measurements, dietary assessment, computational psychometrics, or environmental toxicology as manifested in the paper.

Limit Distribution of the φ-Divergence Based Change Point Estimator

The assumption of stationarity is too restrictive especially for long time series. This paper studies the change point problem through a change point estimator based on the φ-divergence which provides a rich set of distance like measures between pairs of distributions. The change point problem is considered in the following sub-fields: the problem of divergence estimation, testing for the homogeneity between two samples as well as estimating the time of change. The asymptotic distribution of the change point estimator is estimated by the limiting distribution of a stochastic process within given bounds through asymptotic theory surrounding the likelihood theory. The distribution is found to converge to that of a standardized Brownian bridge process.

A Review of Change Point Estimation Methods for Process Monitoring

When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for the different types of changes in the literature. they are: Maximum Likelihood Estimator (MLE), the Cumulative Sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) approaches. This paper gives a synopsis of change point estimation, specifies, categorizes, and evaluates many of the methods that have been recommended for detecting change points in process monitoring. The change points articles in the literature were categorized broadly under five categories, namely: types of process, types of data, types of change, types of phase and methods of estimation. Aside the five broad categories, we also included the parameter involved. Furthermore, the use of control charts and other monitoring tools used to detect abrupt changes in processes were reviewed and the gaps for process monitoring/controlling were examined. A combination of different methods of estimation will be a valuable approach to finding the best estimates of change point models. Further research studies would include assessing the sensitivity of the various change point estimators to deviations in the underlying distributional assumptions.

Convergence of a Randomised Change Point Estimator in GARCH Models

In this paper, the randomised pseudolikelihood ratio change point estimator for GARCH models in [1] is employed and its limiting distribution is derived as the supremum of a standard Brownian bridge. Data analysis to validate the estimator is carried out using the United states dollar (USD)-Ghana cedi (GHS) daily exchange rate data. The randomised estimator is able to detect and estimate a single change in the variance structure of the data and provides a reference point for historic data analysis.

Randomised Pseudolikelihood Ratio Change Point Estimator in Garch Models

In this paper, a randomised pseudolikelihood ratio change point estimator for GARCH model is presented. Derivation of a randomised change point estimator for the GARCH model and its consistency are given. Simulation results that support the validity of the estimator are also presented. It was observed that the randomised estimator outperforms the ordinary CUSUM of squares test, and it is optimal with large variance change ratios.

Common Change-Point Estimation and Changed Panel Isolation after Sequential Detection in an Exponential Family

After a common change point is detected sequentially in N independent panels with observations following a standard exponential family distribution, a BH-type procedure is proposed to isolate the changed panels based on the asymptotic exponential property of CUSUM processes without change with false discovery rate (FDR) control. The common change point is then estimated based on the change-point estimations from the isolated changed panels. Several typical models based on normal, exponential, and Chi-square distributions for detecting changes in mean, rate, and variance are used for illustration with simulation results. A real example with mean or variance change for Dow Jones 30 stock prices is used for illustration.

Testing constant cross-sectional dependence with time-varying marginal distributions in parametric models

Abstract This paper proposes parametric two-step procedures for assessing the stability of cross-sectional dependency measures in the presence of potential breaks in the marginal distributions. The procedures are based on formerly proposed sup-LR tests in which restricted and unrestricted likelihood functions are compared with each other. First, we show theoretically that standard asymptotics do not hold in this situation. We propose a suitable bootstrap scheme and derive test statistics in different commonly used settings. The properties of the test statistics and precision of the associated change-point estimator are analysed and compared with existing non-parametric methods in various Monte Carlo simulations. These studies reveal advantages in test power for higher-dimensional data and an almost uniform superiority of the sup-LR test in terms of precision of the change-point estimator. We then apply this method to equity returns of European banks during the financial crisis of 2008.

Group orthogonal greedy algorithm for change-point estimation of multivariate time series

This paper proposes a three-step method for detecting multiple structural breaks for piecewise stationary vector autoregressive processes. The number of structural breaks can be large and unknown with the locations of the breaks being different among different components. The proposed method is established via a link between a structural break problem and a high-dimensional regression problem. By means of this connection, a group orthogonal greedy algorithm, originated from the high-dimensional variable selection context, is developed for efficiently screening out potential break-points in the first step. A high-dimensional information criterion is proposed for consistent structural breaks estimation in the second step. In the third step, the information criterion further determines the specific components in which structural breaks occur. Monte Carlo experiments are conducted to demonstrate the finite sample performance, and applications to stock data are provided to illustrate the proposed method.

Estimation of change-point for a class of count time series models.

We apply a three-step sequential procedure to estimate the change-point of count time series. Under certain regularity conditions, the estimator of change-point converges in distribution to the location of the maxima of a two-sided random walk. We derive a closed-form approximating distribution for the maxima of the two-sided random walk based on the invariance principle for the strong mixing processes, so that the statistical inference for the true change-point can be carried out. It is for the first time that such properties are provided for integer-valued time series models. Moreover, we show that the proposed procedure is applicable for the integer-valued autoregressive conditional heteroskedastic (INARCH) models with Poisson or negative binomial conditional distribution. In simulation studies, the proposed procedure is shown to perform well in locating the change-point of INARCH models. And, the procedure is further illustrated with empirical data of weekly robbery counts in two neighborhoods of Baltimore City.

Robust Fuzzy Clustering Algorithms for Change-Point Regression Models

This article presents a robust fuzzy procedure for estimating change-point regression models. We propose incorporating the fuzzy change-point algorithm with the M-estimation technique for robust estimations. The fuzzy c partitions concept is embedded into the change-point regression model so the fuzzy c-regressions and fuzzy c-means clustering can be employed to obtain the estimates of change-points and regression parameters. The M estimation with a robust criterion is used to make the estimators robust to the presence of outliers and heavy-tailed distributions. We create two robust algorithms named FCH and FCT by using Huber’s and Tukey’s functions as the robust criterion respectively. Extensive experiments with numerical and real examples are provided for demonstrating the effectiveness and the superiority of the proposed algorithms. The experimental results show the proposed algorithms are resistant to atypical observations and outperform the existing methods. The proposed FCH and FCT are generally comparable but FCT performs better in the presence of extremely high leverage outliers and heavy-tailed distributions. Real data applications show the practical usefulness of the proposed method.

Internal Change Points and External Transmissions

The multiple change points estimation internally identifies the monetary expansion or monetary contraction, the monetary policy interchange, the currency reform breaks, and the routine operational transitions on the multivariate dimensions of the China government bond yields. The external monetary transmissions are separating into the blocks with the conventional monetary policy and zero lower bound period. The recursively identified VAR models are respectively capture the daily interest rate co-movements spreading from the global trends to the destination country in the short run restrictions, the weekly fluctuation transitions from the systematic risks and uncertainty in the financial markets in the medium run, and the monthly compounding interaction mechanism from stock market, government bond market and international monetary transmission in the long run.