EconPapers    
Economics at your fingertips  
 

Divergences Test Statistics for Discretely Observed Diffusion Processes

Alessandro De Gregorio and Stefano Iacus ()
Additional contact information
Alessandro De Gregorio: Università di Milano, Italy

No unimi-1076, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

Abstract: In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete observations $\{X_{t_i}, i=0, \ldots, n\}$ with $t_i = i\Delta_n$, $i=0, 1, \ldots, n$, under the asymptotic scheme $\Delta_n\to0$, $n\Delta_n\to\infty$ and $n\Delta_n^2\to 0$. The class of $\phi$-divergences is wide and includes several special members like Kullback-Leibler, R\'enyi, power and $\alpha$-divergences. We derive the asymptotic distribution of the test statistics based on $\phi$-divergences. The limiting law takes different forms depending on the regularity of $\phi$. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.

Keywords: diffusion processes; empirical level; divergences (search for similar items in EconPapers)
Date: 2008-08-06
Note: oai:cdlib1:unimi-1076
References: Add references at CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://services.bepress.com/unimi/statistics/art38 (application/pdf)

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:bep:unimip:unimi-1076

Access Statistics for this paper

More papers in UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano Contact information at EDIRC.
Bibliographic data for series maintained by Christopher F. Baum ().

 
Page updated 2019-10-03
Handle: RePEc:bep:unimip:unimi-1076