EconPapers    
Economics at your fingertips  
 

A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales

Ole Barndorff-Nielsen (), Svend Erik Graversen, Jean Jacod, Mark Podolskij () and Neil Shephard ()

OFRC Working Papers Series from Oxford Financial Research Centre

Abstract: Consider a semimartingale of the form Y_{t}=Y_0+\int _0^{t}a_{s}ds+\int _0^{t}_{s-} dW_{s}, where a is a locally bounded predictable process and (the "volatility") is an adapted right--continuous process with left limits and W is a Brownian motion. We define the realised bipower variation process V(Y;r,s)_{t}^n=n^{((r+s)/2)-1} \sum_{i=1}^{[nt]}|Y_{(i/n)}-Y_{((i-1)/n)}|^{r}|Y_{((i+1)/n)}-Y_{(i/n)}|^{s}, where r and s are nonnegative reals with r+s>0. We prove that V(Y;r,s)_{t}n converges locally uniformly in time, in probability, to a limiting process V(Y;r,s)_{t} (the "bipower variation process"). If further is a possibly discontinuous semimartingale driven by a Brownian motion which may be correlated with W and by a Poisson random measure, we prove a central limit theorem, in the sense that \sqrt(n) (V(Y;r,s)^n-V(Y;r,s)) converges in law to a process which is the stochastic integral with respect to some other Brownian motion W', which is independent of the driving terms of Y and \sigma. We also provide a multivariate version of these results.

New Economics Papers: this item is included in nep-ecm
Date: 2004
References: Add references at CitEc
Citations: View citations in EconPapers (28) Track citations by RSS feed

Downloads: (external link)
http://www.finance.ox.ac.uk/file_links/finecon_papers/2004fe21.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Working Paper: A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales (2004) Downloads
Working Paper: A central limit theorem for realised power and bipower variations of continuous semimartingales (2004) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sbs:wpsefe:2004fe21

Access Statistics for this paper

More papers in OFRC Working Papers Series from Oxford Financial Research Centre Contact information at EDIRC.
Bibliographic data for series maintained by Maxine Collett ().

 
Page updated 2019-12-05
Handle: RePEc:sbs:wpsefe:2004fe21