Testing Mean Stationarity of Intraday Volatility Curves

We develop a test for mean stationarity of latent volatility curves using high-frequency data. To derive the asymptotic test size and power, we establish a functional invariance principle for semimartingales under a strong mixing condition. The power properties are analyzed under alternatives featuring deterministic trends in the volatility curve dynamics. Application to S\&P 500 futures data provides strong evidence of nonstationary variation in the volatility pattern, with implications for real-time risk management and market activity measurement, including identification of spot volatility and the size of price jumps.