How to identify a trend using Mann-Kendall tests with XLSTAT-Time?

An Excel sheet with both the data and the results can be downloaded by clicking here. The data have been obtained in [Box, G.E.P. and Jenkins, G.M. (1976). Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco], and correspond to monthly international airline passengers (in thousands) from January 1949 to December 1960. It is widely used as a nonstationary seasonal time series. Our goal is to test whether there is a trend in the time series.

After opening XLSTAT, click the Time button in the ribbon and select “Mann-Kendall trend tests” (see below).

Once you've clicked the button, the dialog box appears. Select the data on the Excel sheet. You must select the time series “passengers”. As we selected the column title with the series, we leave the option "Series labels" activated. Two tests can be applied: the classical Mann-Kendall test to test if there is a trend in the time series; the seasonal Mann-Kendall test that takes into account the seasonality in the time series (here 12 months).

In the “options” tab, we select tau<>0 as alternative hypothesis.

Once you have clicked the “OK” button, the computation starts. The results are then displayed.

Interpreting the results of a Mann-Kendall test

The first results displayed by XLSTAT are the basic statistics associated with the time series.

Then, the result of the first test is displayed.

The p-value shows that the null hypothesis is rejected; we can conclude that there is a trend in our time series.

For the second test, we consider the fact that our time series are seasonal with a seasonality of 12 months. The seasonal Mann-Kendall test takes into account the 12 month seasonality and tests whether there is a trend not due to seasonality.

The Kendall's tau is even closer to 1 when we take into account the seasonality. The p-value shows that the null hypothesis is rejected; we can conclude that there is a trend in our time series when we take into account the seasonality.

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