A Nonparametric Trend Test for Seasonal Data With Serial Dependence
TL;DR: In this article, an extension of the Mann-Kendall test for trend in seasonal (e.g., monthly) hydrologic time series is presented, which is robust against nonnormality and censoring.
Abstract: Statistical tests for monotonic trend in seasonal (e.g., monthly) hydrologic time series are commonly confounded by some of the following problems: nonnormal data, missing values, seasonality, censoring (detection limits), and serial dependence. An extension of the Mann-Kendall test for trend (designed for such data) is presented here. Because the test is based entirely on ranks, it is robust against nonnormality and censoring. Seasonality and missing values present no theoretical or computational obstacles to its application. Monte Carlo experiments show that, in terms of type I error, it is robust against serial correlation except when the data have strong long-term persistence (e.g., ARMA (1, 1) monthly processes with ϕ > 0.6) or short records (∼ 5 years). When there is no serial correlation, it is less powerful than a related simpler test which is not robust against serial correlation.
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TL;DR: In this paper, the effect of autocorrelation on the variance of the Mann-Kendall trend test statistic is discussed, and a modified non-parametric trend test is proposed.
2,252 citations
TL;DR: In this article, the power of the Mann-Kendall test and Spearman's rho test for detecting monotonic trends in time series data is investigated by Monte Carlo simulation.
1,642 citations
TL;DR: In this article, the authors investigated the effect of serial correlation on the performance of the Mann-Kendall (MK) statistic and showed that the presence of a trend alters the estimate of the magnitude of serial correlations.
Abstract: This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre-whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre-whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre-whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends. Copyright 2002 Environment Canada. Published by John Wiley & Sons, Ltd.
1,573 citations
TL;DR: In this article, the Mann-Kendall test is modified to account for the effect of scaling in hydrologic data, and the results show a considerable reduction in the number of stations with significant trends when the effects of scaling are taken into account.
981 citations
TL;DR: In this paper, effective sample size (ESS) has been proposed to modify the nonparametric Mann-Kendall (MK) statistical test to assess the significance of trend in hydrological time series.
Abstract: The non-parametric Mann-Kendall (MK) statistical test has been popularly used to assess the significance of trend in hydrological time series The test requires sample data to be serially independent When sample data are serially correlated, the presence of serial correlation in time series will affect the ability of the test to correctly assess the significance of trend To eliminate the effect of serial correlation on the MK test, effective sample size (ESS) has been proposed to modify the MK statistic This study investigates the ability of ESS to eliminate the influence of serial correlation on the MK test by Monte Carlo simulation Simulation demonstrates that when no trend exists within time series, ESS can effectively limit the effect of serial correlation on the MK test When trend exists within time series, the existence of trend will contaminate the estimate of the magnitude of sample serial correlation, and ESS computed from the contaminated serial correlation cannot properly eliminate the effect of serial correlation on the MK test However, if ESS is computed from the sample serial correlation that is estimated from the detrended series, ESS can still effectively reduce the influence of serial correlation on the MK test
878 citations
References
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Book•
01 Jan 1970
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Abstract: From the Publisher:
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.
19,748 citations
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.
Abstract: From the Publisher:
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.
12,650 citations
Book•
01 Jan 1971
TL;DR: Probability Theory. Statistical Inference. Contingency Tables. Appendix Tables. Answers to Odd-Numbered Exercises and Answers to Answers to Answer Questions as discussed by the authors.
Abstract: Probability Theory. Statistical Inference. Some Tests Based on the Binomial Distribution. Contingency Tables. Some Methods Based on Ranks. Statistics of the Kolmogorov-Smirnov Type. References. Appendix Tables. Answers to Odd-Numbered Exercises. Index.
10,382 citations
Book•
01 Jan 1948
TL;DR: The measurement of rank correlation was introduced in this paper, and rank correlation tied ranks tests of significance were applied to the problem of m ranking, and variate values were used to measure rank correlation.
Abstract: The measurement of rank correlation introduction to the general theory of rank correlation tied ranks tests of significance proof of the results of chapter 4 the problem of m ranking proof of the result of chapter 6 partial rank correlation ranks and variate values proof of the result of chapter 9 paired comparisons proof of the results of chapter 11 some further applications.
6,404 citations