XLSTAT: Mann-Kendall trend test in Excel 

 

Dataset for Example

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.

 

Setting Up

• Open XLSTAT.

• Click on the Forecasting/Time series analysis menu and select the Mann-Kendall trend tests feature:

• The Mann-Kendall dialog box appears.

In the General tab:

• Select column B (Passengers) in the Time series field and column A (Month) in the Date data field.

• Leave the option Series labels  activated, as we selected the column headers.

• Activate the Seasonal Mann-Kendall option and enter 12 (=months) in the Period  field (period = number of lags between two seasons).

Note: To calculate the p-value of this test, XLSTAT uses a normal approximation to estimate the distribution of the average Kendall tau. A continuity correction can be also applied if selected by the user.

XLSTAT offers two tests: 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).

• Activate the option Serial dependence. We assume that the series are dependent (eg values of January and February are dependent). 

  

In the Options tab:

• Select  tau<>0 as an alternative hypothesis.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first output displays the descriptive statistics of the series followed by results of the test. In this example, we consider the fact that our time series are characterized by a seasonality of 12 months. The seasonal Mann-Kendall test will tell us whether there is a trend not due to seasonality.

  

The p-value (<0,0001) shows that the null hypothesis is rejected thus we may suggest that there is a significant trend in our time series when we take into account the 12-month seasonality.