Abstract
The monotonic trend tests proposed by Mann (1945), Abelson and Tukey (1963) and Brillinger (1989) are reviewed and evaluated. Simulation experiments using a very large number of simulations are carried out for comparing the Abelson-Tukey and Mann-Kendall tests. The advantages and disadvantages of each test are discussed and the practical implementation and usefulness of these test procedures are clearly demonstrated with some applications to environmental data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abelson, R. P. and Tukey, J. W. (1963) “Efficient utilitzation of non-numerical information in quantitative analysis: general theory and the case of simple order”, The Annals of Mathematical Statistics, 34, 1347–1369.
Box, G. E. P. and Muller, M. E. (1958) A note on the generation of normal deviates, Annals of Mathematical Statistics 28, 610–611.
Bloomfield, P. (1976), Fourier Analysis of Time Series, Wiley, New York.
Brillinger, D. R. (1981), Time Series Data Analysis and Theory, (expanded edition), Holt, Rinehart and Winston, New York.
Brillinger, D. R. (1989), “Consistent detection of a monotonic trend superimposed on a stationary time series”, Biometrika 76, 23–30.
Cleveland, W. S. (1979), “Robust locally weighted regression and smoothing scatter-plots”, Journal of the American Statistical Association 74, 829–836.
Hipel, K. W. and McLeod, A. I. (1994), Time Series Modelling of Environmental and Water Resources Systems, Elsevier, Amsterdam.
Hipel, K. W., McLeod, A. I. and Fosu, P. (1983), “Empirical power comparisons of some tests for trend, in Statistical Aspects of Water Quality Monitoring”, in Develop- ments in Water Science, Volume 27, 347–362, Edited by A.H. El-Shaarawi and R.E.Kwiatkowski.
Hurvich, C. M. (1988), “A mean squared error criterion for time series data windows”, Biometrika 75, 485–490.
Kendall, M. G. and Stuart, A. (1968). The Advanced Theory of Statistics, Volume 3, Hafner, New York.
Kendall, M. G. (1973). Time Series, Griffin, London.
Kendall, M. G. (1975). Rank Correlation Methods (4th ed), Griffin, London. Mann, H. B. (1945), Nonparametric tests against trend, Econometrica 13, 245–259.
Marsaglia, G. (1976), “Random Number Generation”, in Encyclopedia of Computer Science, ed. A. Ralson, pp. 1192–1197, Petrocelli and Charter, New York.
McLeod, A. L and Hipel, K. W. (1994a) The McLeod—Hipel Time Series (MHTS) Package, copyright owned by A. I. McLeod and K. W. Hipel, McLeod—Hipel Research, 121 Longwood Drive, Waterloo, Ontario Canada N2L 4B6, Tel: (519)884–2089.
McLeod, A. I. and Hipel, K. W. (1994b) The McLeod—Hipel Time Series (MHTS) Package Mannual, McLeod—Hipel Research, 121 Longwood Drive, Waterloo, Ontario Canada N2L 4B6, Tel: (519)884–2089.
Tukey, J. W. (1960), “A survey of sampling from contaminated distributions” in Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, Edited by I. O1kin, S. G. Ghurye, W. Hoeffding, W. G. Madow and H. B. Mann, Standford University Press, Standford.
Tukey, J. W. (1967), “An introduction to the calculations of numerical spectrum analysis” in Advanced Seminar on Spectral Analysis of Time Series, edited by B. Harris, pp. 25–46, Wiley, New York.
Valz, P., McLeod, A. I. and Thompson, M. E., (1994a, to appear) “Cumulant generating function and tail probability approximations for Kendall’s score with tied rankings”, Annals of Statistics.
Valz, P., McLeod, A. I. and Thompson, M. E., (1994b, to appear) “Efficient algorithms for the exact computation of significance levels for Kendall’s and Spearman’s scores.”, Journal of Statistical Graphics and Computation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
McLeod, A.I., Hipel, K.W. (1994). Tests for Monotonic Trend. In: Hipel, K.W., McLeod, A.I., Panu, U.S., Singh, V.P. (eds) Stochastic and Statistical Methods in Hydrology and Environmental Engineering. Water Science and Technology Library, vol 10/3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3083-9_19
Download citation
DOI: https://doi.org/10.1007/978-94-017-3083-9_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4379-5
Online ISBN: 978-94-017-3083-9
eBook Packages: Springer Book Archive