EconPapers    
Economics at your fingertips  
 

Nonsynchronous covariation process and limit theorems

Takaki Hayashi and Nakahiro Yoshida

Stochastic Processes and their Applications, 2011, vol. 121, issue 10, 2416-2454

Abstract: An asymptotic distribution theory of the nonsynchronous covariation process for continuous semimartingales is presented. Two continuous semimartingales are sampled at stopping times in a nonsynchronous manner. Those sampling times possibly depend on the history of the stochastic processes and themselves. The nonsynchronous covariation process converges to the usual quadratic covariation of the semimartingales as the maximum size of the sampling intervals tends to zero. We deal with the case where the limiting variation process of the normalized approximation error is random and prove the convergence to mixed normality, or convergence to a conditional Gaussian martingale. A class of consistent estimators for the asymptotic variation process based on kernels is proposed, which will be useful for statistical applications to high-frequency data analysis in finance. As an illustrative example, a Poisson sampling scheme with random change point is discussed.

Keywords: Discrete; sampling; High-frequency; data; Martingale; central; limit; theorem; Nonsynchronicity; Quadratic; variation; Realized; volatility; Stable; convergence; Semimartingale (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (15) Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414910002905
Full text for ScienceDirect subscribers only

Related works:
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:eee:spapps:v:121:y:2011:i:10:p:2416-2454

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Series data maintained by Dana Niculescu ().

 
Page updated 2017-09-29
Handle: RePEc:eee:spapps:v:121:y:2011:i:10:p:2416-2454