I am working with a 100 years time series data of Sea surface temperature. I want to use Mann-Kendall test in trend detection study. But I am worrying about autocorrelation/serial correlation. Does autocorrelation in quit large sample affect the mann-kendall test ?should I use prewhitening to eliminate it? which R package should I prefer to perform the M-K test between Kendall package and modifiedmk package?
The Mann-Kendall test, used to detect a trend in a time series, yields an incorrect (too large) rejection rate when applied to an autocorrelated series with no trend. Prewhitening corrects this situation, but reduces the power of the test when a trend exists.
Ljung and box (1978) based hypothesis testing, also called Q-statistics under different lag size, could be a good practice for investigating whether the individual series are time-independent (i.e., stationary) with no serial correlation or autocorrelation exhibited. Besides this, the non-parametric rank-based Mann-Kendall or M-K test could be helpful in visualising the monotonic trend within the historical series under the null hypothesis (H0) against their alternative hypothesis (H1). In actuality, the presence of autocorrelations increases the variance of residual and could be responsible for minimizing model efficiency.
After investigation, either using Q-statistics or M-K test, if it will result zero autocorrelation (i.e. no serial correlation), which means, no prewhitening will be required.
[https://stat.ethz.ch/R-manual/R-patched/library/stats/html/box.test.html] reference will be helpful in estimating Ljung and box based Q- statistics using R-software [i.e., identification of autocorrelation or serial correlation].
M-K test can be perform using the package "Kendall" of the R-software.
if series having positive autocorrelation modified Mann-Kendal test(Non-Parametric test ) more suitable compare to Mann-Kendal test to study the trend in large data set. we can use Package ‘modifiedmk’ in the r program for the following study.
Ok but the package ‘modifiedmk’ contains several functions. I recommend reading carefully the papers mentioned to select the one which is the most adequate. Another option would be to find a more appropriate method. This is difficult without having the data.
Dear Khandoker Rakib Hossain ,
Most hydro-climatic time series demonstrate serial dependency, especially temperature-related parameters such as SST. However, I suggest checking your SST data for autocorrelation, beforehand (such as >>autocorr in MATLAB or...).
If there exists visible autocorrelation, then it MUST be removed before checking for possible trends. Mann-Kendall trend test is a non-parametric test; meaning that your data (be it for 100 years or 30 years) should not follow any specific distribution, and should not demonstrate serial dependency and seasonality.
Thank you so much dear @Roshanak Tootoonchi. It's a very helpful answer.
Dear Khandoker Rakib Hossain
For the series with significant autocorrelation coefficients, you can use the modified Mann-Kendall (M-K) method by Hamed and Rao (1998). This is due to the fact that the existence of positive (negative) serial correlation will increase (decrease) the possibility of rejecting the null hypothesis of no trend while it is actually true (Tabari and Hosseinzadehtalaei, 2011).
For more information you may read these articles:
Article Temporal variability of precipitation over Iran: 1966-2005
Article A Modified Mann-Kendall Trend Test for Autocorrelated Data
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