  We consider the moderate deviations behaviors for two (co-) volatility
estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The
results are obtained by using a new result about the moderate deviations
principle for m-dependent random variables based on the Chen-Ledoux type
condition. In the last decade there has been a considerable development of the
asymptotic theory for processes observed at a high frequency. This was mainly
motivated by financial applications , where the data, such as stock prices or
currencies, are observed very frequently. As under the no-arbitrage assumptions
price processes must follow a semimartingale, there was a need for
probabilistic tools for functionals of semimartingales based on high frequency
observations. Inspired by potential applications, probabilists started to
develop limit theorems for semimartingales. Statisticians applied the
asymptotic theory to analyze the path properties of discretely observed
semimartingales: for the estimation of certain volatility functionals and
realised jumps, or for performing various test procedures. We consider X t = (X
1,t , X 2,t) t$\in$[0,T ] a 2-dimensional semimartingale, defined on the
filtred probability space ($\Omega$, F , (F t) [0,T ] , P), of the form
