Nonparametric Approach to Detecting Seasonality in Time Series: Application of the Kruskal-Wallis (KW) Test on Tourist Arrivals to Sri Lanka

This study applies the nonparametric Kruskal-Wallis (KW) test to determine the presence of seasonality in time series data of tourist arrivals in Sri Lanka. It illustrates the mechanism of the KW test for detecting seasonality in auto correlated data. The KW was originally developed for cross-sectional data with relevant assumptions to investigate the median differences between groups. Therefore, the KW test needs modifications and new assumptions to employ with time series data. Thus, the current research empirically evaluates the use of the test for detecting the seasonality of a time series using quarterly tourist arrivals to Sri Lanka from 1990 to 2019. As suggested in the study, formal unit root tests were conducted to trace stationarity and results of the ADF tests have shown that the original data are non-stationary while the first differences are stationary at the 5 per cent level of significance. The findings divulge that the Kruskal-Wallis test is versatile and can precisely detect the seasonality of a time series after making necessary treatments to the data to fulfil the assumptions. This study provides added graphical presentations of seasonal dynamics to strengthen the use of the test. In addition, the post hoc test provided more information on the statistical significance of the dynamics of seasonality. The Kruskal-Wallis test does not supply seasonal indices, which is a primary disadvantage of the test. Therefore, the current research proposed to use an amalgamation of other time series approaches with the Kruskal-Wallis test.