I have a Annual Rainfall time series data (1987-2017). I am determining the trend in the data using MK test. However I found that if there is a serial correlation we should go for MMK test.
Therefore I calculated correlation coefficient at different lags for the original data (upto10 lags) and found that the correlation coefficient are within the tolerance band (within upper limit and lower limit at 5 % significance level) except at lag 4 it is above Upper limit.
Does this mean the series is autocorrelated?
What is the criteria for going for MMK test?
Do we really need to perform student t test corresponding to lag 1 correlation coefficient? Is this test justifiable?
This makes me confused because at lag 1 there is no auto correlation (it is within tolerance band) however at lag 4 there is auto correlation.
So there is mismatch. Student t test would entail no autocorrelation whereas the correlation coefficient at lag 4 entails there is auto correlation.
Your help would be appreciated
Hi,
Time-series data are often lacking serial independence. Positive serial correlation inflates the variance of the estimated time-series mean and, therefore, the time-series contains less information about the mean than a random series. The serial correlation coefficient aids the validation of time-series independence.
If serial correlation is found to be present in a time-series then the process of pre-whitening data may be performed. Pre-whitening a time-series removes a serial correlation component such as an auto-regressive process (red noise) prior to applying the trend detection test.
Modified Mann-Kendall test (MMK) pre-whitening has been used to detect a trend in a time series in the presence of auto-correlation. Since pre-whitening may reduce the
detection rate of significant trend in the Mann-Kendall (MK) test, the Modified Mann-Kendall (MMK) test is employed for trend detection of an auto-correlated series. Only the significant values of the auto-correlation function of ranks of the observations are used to calculate the variance correction factor, as the variance of the Mann-Kendall test statistic is underestimated when data are positively auto-correlated.
Oluwafemi Adeyeri Thank you for the response but How do we know that the time series has serial autocorrelation? What should be the limiting criterial to proceed with MMK test
Well,
For series autocorrelation, you can use the method of Chatfield 1989.
Good luck
@Vasker Sharma, you can use the autocorrelation fuction syntax in R,that is acf (), assuming you have a monthly data series of a data frame called Rubi, to check for auto correlation at lag=1 in the January series of Rubi in R you type as follows;
acf (Rubi$January,lag.max=1)$acf pressing your enter key will display the autocorrelation plot at lag=1,you will clearly see the limit line marked in blue,if your output crosses the limit line in either the positive or negative side of the divide then you can say that the January series of the data frame called Rubi is statistically significant at lag=1.Modified Mann-Kendall (MMK) is then recommended,in such case i will recommend the Bias Corrected Pre-whitening (BCPW).
Best of luck
@Christian Njoku. Thank you. Now it is much clearer to me. Many thanks
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