Email this article Change-point detection in environmental time series based on the informational approach
Abstract
In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The data seasonality structure is incorporated through a linear modeling approach. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.
References
Alpuim, T. and El-Shaarawi, A. (2009). Modeling monthly temperature data in Lisbon and Prague. Environmetrics, 20(7).
Antoch, J., uˇkova, M. H. and Pr ́aˇskov ́a, Z. (2009). Effect of dependence on statistics for determination of change. Journal of Statistical Planning and Inference, 60.
Akaike H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle. In Proceedings of the 2nd International Symposium of Information Theory, pages 267–281. Akademic Kiado.
Barratt, B., Atkinson, R., Anderson, H.R., Beevers, S., Kelly, F., Mudway, I. and Wilkinson, P. (2007). Investigation into the use of the CUSUM technique in identifying changes in mean air pollution levels following introduction of a traffic management scheme. Atmospheric Environment, 41.
Beaulieu, C., Chen, J. and Sarmiento, J.L. (2012). Change-point analysis as a tool to detect abrupt climate variations. Philosophical Transactions of the Royal Society A, 370.
Bozdogan, H. (1987). Model selection and Akaike’s Information criterion (AIC): The general theory and its analytical extension. Psychometrika, 52.
Bozdogan, H., Sclove, S.L. and Gupta, A.K. (1994). AIC-Replacements for some mul- tivariate tests of homogeneity with applications in multisample clustering and vari- able selection. In Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach, volume 2, pages 199–232. Kluwer Academic.
Caussinus, H. and Mestre, O. (2004). Detection and correction of artificial shifts in climate series. Journal of the Royal Statistical Society: Series C, 53.
Chen, J. (1998). Testing for a change point in linear regression models. Communications in Statistics - Theory and Methods, 27.
Chen, J. and Gupta, A.K. (1997). Testing and Locating variance Changepoints with Application to Stock Prices. Journal of the American Statistical Association, 92.
Chen, J. and Gupta, A.K. (1997). Change point analysis of a Gaussian model. Statistical Papers, 40.
Chen, J. and Gupta, A.K. (2001). On change point detection and estimation. Commu- nications in Statistics - Simulation and Computation, 30.
Chen, J. and Gupta, A.K. (2012). Parametric Statistical Change Point analysis. Birkhauser.
Chernoff, H. and Zacks, S. (1964). Estimating the current mean of a normal distribution which is subject to changes in time. Annals of Mathematical Statistics, 35.
Chu, H.J., Pan, T.Y. and Liou, J.J. (2012). Change-point detection of long-duration ex- treme precipitation and the effect on hydrologic design: a case study of south Taiwan. Stochastic Environmental Research and Risk Assessment, 26.
Costa, M. and Gonc ̧alves, AM. (2011). Clustering and forecasting of dissolved oxygen concentration on a river basin. Stochastic Environmental Research and Risk Assess- ment, 25.
Davis, R.A., Lee, T.C.M. and Rodriguez-Yam, G.A. (2006). Structural break estimation for non- stationary time series models. Journal of the American Statistical Association, 101.
El-Shaarawi, A.H. and Esterby, S.R. (1982). Inference About the Point of Change in A Regression Model With A Stationary Error Process. In Proceedings of an Interna- tional Conference Held at Canada Centre for Inland Waters, Time Series Methods in Hydrosciences, pages 55–67.
Gon ̧calves, A.M. and Alpuim, T. (2011). Water quality monitoring using cluster analysisand linear models. Environmetrics, 22.
Gon ̧calves, A.M. and Costa, M. (2011). Application of Change-Point Detection to a Structural Component of Water Quality Variables. In Proceedings of the Interna- tional Conference on Numerical Analysis and Applied Mathematics, volume 1389, pages 1565–1568. AIP Conference Proceedings.
Gon ̧calves, A.M. and Costa, M. (2013). Predicting seasonal and hydro-meteorological impact in environmental variables modelling via Kalman filtering. Stochastic Envi- ronmental Research and Risk Assessment, 27.
H ́ajek, J. (1962). Asymptotically most powerful rank order tests. Annals of Mathematical Statistics, 33.
Hawkins, D.M. (1977). Testing a sequence of observations for a shift in location. Journal of the American Statistical Association, 72.
Hawkins, D.M. and Zamba, K.D. (2005). Statistical process control for shifts in mean or variance using a changepoint formulation. Technometrics, 42.
Hsu, D.A. (1977). Tests for Variance Shift at an Unknown Time Point. Journal of the Royal Statistical Society: Series C, 26.
Incl ́an, C. and Tiao, G.C. (1994). Use of cumulative sums of squares for retrospective detection of changes of variance. Journal of the American Statistical Association, 89.
Jaruˇskov ́a, D. (1996). Change-Point Detection in Meteorological Measurement. Monthly Weather Review, 124.
Jaruˇskov ́a, D. (1997). Some problems with application of change-point detection methods to environmental data. Environmetrics, 8.
Jaruˇskov ́a, D. and Rencov, M. (2008). Analysis of annual maximal and minimal tem- peratures for some European cities by change point methods. Environmetrics, 19.
Jaruˇskov ́a, D. (2010). Asymptotic behavior of a test statistic for detection of change in mean of vectors. Journal of Statistical Planning and Inference, 140.
Krishnaiah, P.R. and BQ Miao, B.Q. (1988). Review about Estimation of Change Points. Handbook of Statistics 7, Elsevier.
Kitagawa, G. (1979). On the use of AIC for the detection of outliers. Technometrics, 21.
Li, S. and Lund, R.B. (2012). Multiple Changepoint Detection via Genetic Algorithms. Journal of Climate, 25.
Lu, Q., Lund, R.B. and Lee, T.C.M. (2010). An MDL Approach to the Climate Seg- mentation Problem. Annals of Applied Statistics, 4.
Lund, R. and Reeves, J. (2002). Detection of Undocumented Changepoints: A Revision of the Two-Phase Regression Model. Journal of Climate, 15.
Lund, R. Wang, X.L., Lu, Q.Q.,Reeves L., Gallagher, C. and Feng, Y. (2007). Change- point Detection in Periodic and Autocorrelated Time Series. Journal of Climate, 20.
R Development Core Team (2011). R: A Language and Environment for Statistical Com- puting. R Foundation for Statistical Computing, Vienna. http//www.R-project.org
Rao, C.R. and Wu, Y. (1989). A strongly consistent procedure for model selection in a
regression problem. Biometrika, 76.
Schwarz, G. (1989). Estimating the dimension of a model. Annals of Statistics, 6.
Srivastava, M.S. and Worsley, K.J. (1986). Likelihood ratio test for a change in the multivariate normal mean. Journal of the American Statistical Association, 81.
Vostrikova, L.J. (1986). Detecting ’disorder’ in multidimensional random processes. Soviet Mathematics Doklady, 24.
Worsley, K.J. (1979). On the likelihood ratio test for a shift in location of normal populations. Journal of the American Statistical Association, 74.
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