U.S. Department of Commerce

Research Reports

You are here: Census.govSubjects A to ZResearch Reports Sorted by Year › Abstract of RRS2013/06
Skip top of page navigation

Fitting Constrained Vector Autoregression Models

Tucker McElroy and David Findley


This paper expands the estimation theory for both quasi-maximum likelihood estimates (QMLEs) and Least Squares estimates (LSEs) for potentially misspecified constrained VAR(p) models. Our main result is a linear formula for the QMLE of a constrained VAR(p), which generalizes the Yule-Walker formula for the unconstrained case. We make connections with the known LSE formula and the determinant of the forecast mean square error matrix, showing that the QMLEs for a constrained VAR(p) minimize this determinant; however, the QMLEs need not minimize the component entries of the mean square forecast error matrix, in contrast to the unconstrained case. An application to computing mean square forecast errors from misspecified models is discussed, and numerical comparisons of the different methods are presented and explored.


Tucker McElroy and David Findley. (2013). Fitting Constrained Vector Autoregression Models. Center for Statistical Research & Methodology Research Report Series (Statistics #2013-06). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2013-06.pdf>.

Source: U.S. Census Bureau, Center for Statistical Research & Methodology

Published online: September 25, 2013
Last revised: September 25, 2013


[PDF] or PDF denotes a file in Adobe’s Portable Document Format. To view the file, you will need the Adobe® Reader® Off Site available free from Adobe.

This symbol Off Site indicates a link to a non-government web site. Our linking to these sites does not constitute an endorsement of any products, services or the information found on them. Once you link to another site you are subject to the policies of the new site.

Source: U.S. Census Bureau | Research and Methodology Directorate | Center for Statistical Research & Methodology | (301) 763-3215 (or chad.eric.russell@census.gov) |   Last Revised: November 15, 2013