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...

A test for serial independence is proposed which is related to the BDS test but focuses on tail event probabilities rather than probabilities near the center of the distribution. The motivation behind this approach is to obtain a test more suitable for detecting structure in the tails, such as...