A Generalised Seasonality Test and Applications for Cryptocurrency and Stock Market Seasonality

This study develops a novel generalised seasonality test that utilises sequential dummy variable regressions for seasonality periodicity equal to prime numbers. It allows to test for existence of any seasonal patterns against the broad null hypothesis of no seasonality and to isolate most prominent seasonal cycles while using harmonic mean p-values to control for multiple testing. The proposed test has numerous applications in time series analysis. As an example, it is applied to identify seasonal patterns in 76 national stock markets and 772 cryptocurrency markets to detect trading cycles, determine their length, and test the weak-form efficient market hypothesis. Cryptocurrency markets are shown to be less efficient than national stock markets, with predominantly irregular seasonality periodicity that cannot be reduced to conventional weekly, monthly, or annual cycles.