Institute of Mathematical Statistics Lecture Notes - Monograph Series

Order determination in general vector autoregressions

Bent Nielsen

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In the application of autoregressive models the order of the model is often estimated using either a sequence of likelihood ratio tests, a likelihood based information criterion, or a residual based test. The properties of such procedures has been discussed extensively under the assumption that the characteristic roots of the autoregression are stationary. While non-stationary situations have also been considered the results in the literature depend on conditions to the characteristic roots. It is here shown that these methods for lag length determination can be used regardless of the assumption to the characteristic roots and also in the presence of deterministic terms. The proofs are based on methods developed by C. Z. Wei in his joint work with T. L. Lai.

Chapter information

Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai, eds., Time Series and Related Topics: In Memory of Ching-Zong Wei (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 93-112

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F10: Point estimation

autoregression lag length information criteria

Copyright © 2006, Institute of Mathematical Statistics


Nielsen, Bent. Order determination in general vector autoregressions. Time Series and Related Topics, 93--112, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000978.

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