How to Perform a Mann-Kendall Trend Test in Python

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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.

H_A (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)

timese

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.

Additional Resources

How to Plot a Time Series in Matplotlib
How to Perform an Augmented Dickey-Fuller Test in Python
How to Plot Multiple Series from a Pandas DataFrame