A Mann-Kendall Trend Test is used to determine whether or not a trend exists in time series data. It is a non-parametric test, meaning there is no underlying assumption made about the normality of the data.
The hypotheses for the test are as follows:
H0 (null hypothesis): There is no trend present in the data.
HA (alternative hypothesis): A trend is present in the data. (This could be a positive or negative trend)
If the p-value of the test is lower than some significance level (common choices are 0.10, 0.05, and 0.01), then there is statistically significant evidence that a trend is present in the time series data.
This tutorial explains how to perform a Mann-Kendall Trend Test in Python.
Example: Mann-Kendall Trend Test in Python
To perform a Mann-Kendall Trend Test in Python, we will first install the pymannkendall package:
pip install pymannkendall
Once we’ve installed this package, we can perform the Mann-Kendall Trend Test on a set of time series data:
#create dataset data = [31, 29, 28, 28, 27, 26, 26, 27, 27, 27, 28, 29, 30, 29, 30, 29, 28] #perform Mann-Kendall Trend Test import pymannkendall as mk mk.original_test(data) Mann_Kendall_Test(trend='no trend', h=False, p=0.422586268671707, z=0.80194241623, Tau=0.147058823529, s=20.0, var_s=561.33333333, slope=0.0384615384615, intercept=27.692307692)
Here is how to interpret the output of the test:
- trend: This tells the trend. Possible output includes increasing, decreasing, or no trend.
- h: True if trend is present. False if no trend is present.
- p: The p-value of the test.
- z: The normalize test statistic.
- Tau: Kendall Tau.
- s: Mann-Kendal’s score
- var_s: Variance S
- slope: Theil-Sen estimator/slope
- intercept: Intercept of Kendall-Theil Robust Line
The main value we’re interested in is the p-value, which tells us whether or not there is a statistically significant trend in the data.
In this example, the p-value is 0.4226 which is not less than .05. Thus, there is no significant trend in the time series data.
Along with performing the Mann-Kendall Trend test, we can create a quick line plot using Matplotlib to visualize the actual time series data:
import matplotlib.pyplot as plt plt.plot(data)
From the plot we can see that the data is a bit all over the place, which confirms that there is no clear trend in the data.