Stationarity Testing in High-Frequency Seasonal Time Series

Deciding whether seasonality is of a stochastic nature, and thus slowly changing over time, or deterministic and thus repeating in the same way each season can have a substantial impact on forecast accuracy. Tests for stochastic seasonality, called seasonal unit root tests, have been developed for certain common seasonal periods, like 12 (monthly data) 4 and 2, but until now have not been available for high frequency (like daily data over years or minute by minute over days). This paper fills the gap, arriving at a simpler distributional result than is usually the case with unit roots. An example using natural gas supply is used to illustrate.