Testing for Stationarity of Volatility Curves

We develop a test for stationarity of latent volatility curves over time using high-frequency financial data. For deriving the asymptotic size and power of the test, we establish a functional invariance principle for semimartingales under a strong mixing condition. The power properties of our proposed feasible test are analyzed under alternative hypotheses featuring deterministic trends in the volatility curve dynamics. Simulation results corroborate our theoretical findings. Application of the test to high-frequency S&P 500 futures data provides strong evidence of nonstationary variation in the intraday volatility pattern over time.