We discuss inference on the Lévy measure in case of noisy observations. An extension of the pre-averaging method allows for a consistent estimation of the associated spectral function. The asymptotic behaviour of the novel estimator is the same as without noise.

Most previous studies examine the relationship between stock market returns and volatility using low frequency data such as daily or weekly basis. In this study, using the high frequency intraday data, we expand the scope of prior studies to investigate the relationship of short-term changes of...

The paper aims to suggest the best volatility forecasting model for stock markets in Turkey. The findings of this paper support the superiority of high frequency based volatility forecasting models over traditional GARCH models. MIDAS and HAR-RV-CJ models are found to be the best among high...

This paper proposes a robustification of the test statistic of Aït-Sahalia and Jacod (2009b) for the presence of market microstructure noise in high frequency data, based on the pre-averaging method of Jacod et al. (2010). We show that the robustified statistic restores the test’s...

The Epps effect, the decrease of correlations between stock returns for short time windows, was traced back to the trading asynchronicity and to the occasional lead-lag relation between the prices. We study pairs of stocks where the latter is negligible and confirm the importance of...

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed by...

We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ϵσ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process...

In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary (BSS) processes. More precisely, we will show that singularities in the weight function, which is one of the ingredients of a BSS process, may lead to non-standard limits of the...

The estimation of local characteristics of Itô semimartingales has received a great deal of attention in both academia and industry over the past decades. In various papers limit theorems were derived for functionals of increments and ranges in the infill asymptotics setting. In this paper we...

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies...