Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications

Yong Bao and Aman Ullah

No 200907, Working Papers from University of California at Riverside, Department of Economics

Abstract: We derive some new results on the expectation of quadratic forms in normal and nonnormal variables. Using a nonstochastic operator, we show that the expectation of the product of an arbitrary number of quadratic forms in noncentral normal variables follows a recurrence formula. This formula includes the existing result for central normal variables as a special case. For nonnormal variables, while the existing results are available only for quadratic forms of limited order (up to 3), we derive analytical results to a higher order 4. We use the nonnormal results to study the effects of nonnormality on the finite sample mean squared error of the OLS estimator in an AR(1) model and the QMLE in an MA(1) model.

Keywords: Expectation; Quadratic form; Nonnormality (search for similar items in EconPapers)
JEL-codes: C10 C19 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2009-06, Revised 2009-06
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://economics.ucr.edu/repec/ucr/wpaper/09-07.pdf First version, 2009 (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:ucr:wpaper:200907

Access Statistics for this paper

More papers in Working Papers from University of California at Riverside, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Kelvin Mac ().