Recent studies show that the zero-process of observed intraday financial returns is frequently characterised by non-stationary periodicity. As liquidity varies across the trading day, not only does unconditional volatility change, but also the unconditional zero-probability. While scaling returns by the time-varying intraday volatility may stabilise volatility, it does not make the zero-process of scaled returns stationary. This invalidates standard methods of risk estimation, and recent studies document that the use of such invalid methods can have major effects on risk estimates. Formal tests for non-stationary periodicity in the zero-process can therefore be of great value in guiding the choice of a suitable risk estimation procedure. Despite this, little attention has been devoted to the derivation of such tests. Here, we help filling this gap by developing user-friendly yet flexible and powerful tests that hold under mild assumptions. Next, an empirical study reveals that intraday financial returns are widely characterised by non-stationary periodicity in the zero-process. This has important and potentially wide-ranging implications for future research

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