Change-Point Methods
Abdel H. El-shaarawi,
Abdel H. El-shaarawi
National Water Research Institute, Burlington, Ontario, Canada
McMaster University, Ontario, Canada
The American University in Cairo, Cairo, Egypt
Search for more papers by this authorAbdel H. El-shaarawi,
Abdel H. El-shaarawi
National Water Research Institute, Burlington, Ontario, Canada
McMaster University, Ontario, Canada
The American University in Cairo, Cairo, Egypt
Search for more papers by this authorAbstract
This article reviews recent applications of change-point methods for modeling nonstationarities in environmental data. In particular, maximum likelihood-based methods for the detection and estimation of parameter changes at unknown times in environmental time series data are emphasized.
References
- 1 Jarusková, D. (1996). Change-point detection in meteorological measurement, Monthly Weather Review 124, 1535–1543.
- 2 Reeves, J., Chen, J., Wang, X.L., Lund, R., & Lu Q. (2007). A review and comparison of change point detection techniques for climate data, Journal of Applied Meteorology and Climatology 45, 900–915.
- 3 Jandhyala, V.K., Zacks, S., & El-Shaarawi, A.H. (2000). Change-point methods and their applications: contributions of Ian MacNeill, Environmetrics 10, 657–676.
- 4
Chen, J. &
Gupta, A.K.
(2012).
Parametric Statistical Change Point Analysis,
Springer,
Boston.
10.1007/978-0-8176-4801-5 Google Scholar
- 5 Csörgo, M. & Horváth, L. (1997). Limit Theorems in Change-Point Analysis, John Wiley & Sons, Inc., Chichester.
- 6 Davis, R.A., Huang, D., & Yao, Y.C. (1995). Testing for a change in the parameter values and order of an auto-regressive model, The Annals of Statistics 23, 282–304.
- 7 Horváth, L., Kokoszka, P., & Steinebach, J. (1999). Testing for changes in multivariate dependent observations with an application to temperature changes, Journal of Multivariate Analysis 68, 96–119.
- 8 Beckage, B., Joseph L., Bélisle, P., Wolfson, D., & Platt, W., (2007). Bayesian change-point analysis in ecology, New Phytologist 174, (2), 456–467.
- 9
El-Shaarawi, A.H. &
Esterby, S.R.
(1982).
Inference about the point of change in a regression model with a stationary error process,
Developments in Water Science
17,
55–127.
10.1016/S0167-5648(08)70701-9 Google Scholar
- 10
Esterby, S.R. &
El-Shaarawi, A.H.
(1981).
Inference about the point of change in a regression model,
Applied Statistics
30,
277–285.
10.2307/2346352 Google Scholar
- 11 Jarrett, R.C. (1979). A note on the intervals between coal-mining disasters, Biometrika 66, 191–193.
- 12 Lund, R & Reeves, J (2002). Detection of undocumented change points: a revision of the two-phase regression model, Journal of Climate 15, 2547–2554.
- 13 Miller, K.A. & Glantz, M.H. (1988). Climate and economic competitiveness: Florida freezes and the global citrus processing industry, Climate Change 12, 135–164.
- 14 Potter, K.W. (1981). Illustration of a new test for detecting a shift in mean precipitation series, Monthly Weather Review 109, 2040–2045.
- 15 Turner, J., Lachlan-Cope, T.A., Colwell, S., Marshell, G.J., & Connolley, W.M. (2006). Significant warming of the Antarctic winter troposphere, Science 311, 1914–1917.
- 16 Gombay, E. & Horváth, L. (1994). An application of the maximum likelihood test to the change-point problem, Stochastic Processes and Their Applications 50, 161–171.
- 17 Gombay, E. & Horváth, L. (1997). An application of the likelihood method to change-point detection, Environmetrics 8, 459–467.
- 18 Hawkins, D.M. (1977). Testing a sequence of observations for a shift in location, Journal of the American Statistical Association 72, 180–186.
- 19 Yao, Y.C. & Davis, R.A. (1986). The asymptotic behavior of the likelihood ratio statistic for testing a shift in mean in a sequence of independent normal variates, Sankhyā, Series A 48, 339–353.
- 20 Worsley, K.J. (1986). Confidence regions and tests for a change-point in a sequence of exponential family random variables, Biometrika 73, 91–104.
- 21 Jandhyala, V.K., Fotopoulos, S.B., & Hawkins, D.M. (2002). Detection and estimation of abrupt changes in the variability of a process, Computational Statistics and Data Analysis 40, 1–19.
- 22 Jaruskova, D. (1997). Some problems with application of change-point detection methods to environmental data, Environmetrics 8, 469–483.
- 23 Katz, R.W. & Brown, B.G. (1992). Extreme events in a changing climate: variability is more important than averages, Climatic Change 21, 289–302.
- 24 Glantz, M.H. (1987). Drought and Hunger in Africa: Denying Famine a Future, Cambridge University Press, Cambridge.
- 25 Mearns, L.O., Katz, R.W., & Schneider, S.H. (1984). Extreme high temperature events: changes in their probabilities with changes in mean temperature, Journal of Climatology and Applications in Meteorology 23, 1601–1613.
- 26 MacNeill, I.B., Tang, S.M., & Jandhyala, V.K. (1991). A search for the source of the Nile's change-points, Environmetrics 2, 341–375.
- 27 Cobb, G.W. (1978). The problem of the Nile: conditional solution to a change-point problem, Biometrika 62, 243–251.
- 28 Brillinger, D.R. (1994). Some river wavelets, Environmetrics 5, 211–220.
- 29 Brillinger, D.R. (1997). Random process methods and environmental data: the 1996 Hunter Lecture, Environmetrics 8, 269–281.
- 30
Shiryaev, A.N.
(1963).
On optimum methods in quickest detection problems,
Theory of Probability and its Applications
8,
22–46.
10.1137/1108002 Google Scholar
- 31 Chernoff, H. & Zacks, S. (1964). Estimating the current mean of a normal distribution, which is subjected to change in time, Annals of Mathematical Statistics 35, 999–1018.
- 32 Hinkley, D.V. (1970). Inference about the change-point in a sequence of random variables, Biometrika 57, 1–17.
- 33 Hinkley, D.V. (1972). Time ordered classification, Biometrika 59, 509–523.
- 34 Jandhyala, V.K. & Fotopoulos, S.B. (1999). Capturing the distributional behavior of the maximum likelihood estimate of a change-point, Biometrika 86, 129–140.
- 35 Fotopoulos, S.B. & Jandhyala, V.K. (2001). Maximum likelihood estimation of a change-point for exponentially distributed random variables, Statistics and Probability Letters 51, 423–429.
- 36 Fotopoulos, S.B., Jandhyala, V., & Khapalova, E. (2011). Change-point mle in the rate of exponential sequences with application to Indonesian seismological data, Journal of Statistical Planning and Inference 141, 220–234.
- 37 Jandhyala, V.K., Fotopoulos, S.B., & Evagelopoulos, N. (2000). A comparison of unconditional and conditional solutions to the maximum likelihood estimation of a change-point, Computational Statistics and Data Analysis 34, 315–334.
- 38 Lee, C.B. (1998). Bayesian analysis of a change-point in exponential families with applications, Computational Statistics and Data Analysis 27, 195–205.
- 39 Asmussen, S. (1985). Applied Probability and Queues, John Wiley & Sons, New York.
- 40 Veraverbeke, N. & Teugels, J.T. (1975). The exponential rate of convergence of the distribution of the maximum of a random walk, Journal of Applied Probability 12, 279–288.
- 41 Downham, D.Y. & Fotopoulos, S.B. (1981). Some inequalities on the distribution of ladder epochs, Journal of Applied Probability 18, 770–775.
- 42 Stoyan, D. (1976). Comparison Methods for Queues and Other Stochastic Models, John Wiley & Sons, New York.
- 43 Maguire, B.A., Pearson, E.S., & Wynn, A.H.A. (1952). The time intervals between industrial accidents, Biometrika 38, 168–180.
- 44 Siegmund, D. (1988). Confidence sets in change-point problems, International Statistical Review 56, 31–48.
- 45
Leadbetter, M.R.,
Lindgren, G., &
Rootzen, H.
(1983).
Extremes and Related Properties of Random Sequencies and Processes,
Springer-Verlag,
New York.
10.1007/978-1-4612-5449-2 Google Scholar
- 46 Jandhyala, V.K., Fotopoulos, S.B., & Evagelopoulos, N. (2000). Change-point methods for Weibull models with applications to detection of trends in extreme temperatures, Environmetrics 10, 547–564.
Further Reading
- Briggs, W.M. (2008). On the changes in the number and intensity of North Atlantic tropical cyclones, Journal of Climate 27, 1387–1402.
- Veraverbeke, N. & Teugels, J.T. (1976). The exponential rate of convergence of the distribution of the maximum of a random walk. Part II, Journal of Applied Probability 13, 733–740.
