Testing and Detecting Jumps Based on a Discretely Observed Process

39 Pages Posted: 6 Jan 2009

See all articles by Yingying Fan

Yingying Fan

University of Southern California - Marshall school of Business

Jianqing Fan

Princeton University - Bendheim Center for Finance

Date Written: December 19, 2008

Abstract

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test statistic in A\"{i}t-Sahalia and Jacod (2007), our new test statistic enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. Thanks to the reduction of the variance, we also propose a new test procedure to identify the locations of jumps. The problem of jump identification thus reduces to a multiple comparison problem. We employ the False Discovery Rate (FDR) approach to control the type I error. Simulation studies and real data analysis further demonstrate the power of the newly proposed test method.

Keywords: Jump diffusion process, test for jumps, high frequency, stable convergence, FDR

JEL Classification: C12, C14

Suggested Citation

Fan, Yingying and Fan, Jianqing, Testing and Detecting Jumps Based on a Discretely Observed Process (December 19, 2008). Available at SSRN: https://ssrn.com/abstract=1184442 or http://dx.doi.org/10.2139/ssrn.1184442

Yingying Fan (Contact Author)

University of Southern California - Marshall school of Business ( email )

Marshall School of Business
BRI 401, 3670 Trousdale Parkway
Los Angeles, CA 90089
United States

HOME PAGE: http://www-rcf.usc.edu/~fanyingy

Jianqing Fan

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

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