Karhunen–Loeve expansions for the detrended Brownian motion
The detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the subspace spanned by linear functions. Karhunen–Loeve expansion for the process is obtained, together with the explicit formula for the Laplace transform of the squared L2 norm. Distribution identities are established in connection with the second order Brownian bridge developed by MacNeill (1978). As applications, large and small deviation asymptotic behaviors for the L2 norm are given.
Volume (Year): 82 (2012)
Issue (Month): 7 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nyblom, Jukka & Harvey, Andrew, 2000.
"Tests Of Common Stochastic Trends,"
Cambridge University Press, vol. 16(02), pages 176-199, April.
- Li, Wenbo V., 1992. "Limit theorems for the square integral of Brownian motion and its increments," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 223-239, June.
- Niklas Ahlgren & Jukka Nyblom, 2008. "Tests against stationary and explosive alternatives in vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 421-443, 05.
- Bart Hobijn & Philip Hans Franses & Marius Ooms, 2004. "Generalizations of the KPSS-test for stationarity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 483-502.
- A. M. Robert Taylor, 2003. "Locally Optimal Tests Against Unit Roots in Seasonal Time Series Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 591-612, 09.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1235-1241. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.