We consider limit theorems for variations of high frequency data under the finite time horizon. The error distributions are asymptotically mixed normal. The non-ergodic martingale expansion is applied to the p-variation and the realized volatility with microstructure noise. References Yoshida, N.: Martingale expansion in mixed normal limit. arXiv (2012), Stochastic Processes and their Applications (2013) Yoshida, N.: Asymptotic expansion for the quadratic form of the diffusion process. arXiv (2012) Podolskij, M., Yoshida, N.: Edgeworth expansion for functionals of continuous diffusion processes, to appear in Annals of Applied Probability (2016) Podolskij, M., Veliyev, B., Yoshida, N.: Edgeworth expansion for the pre-averaging estimator. arXiv (2015).