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Some remarks on regression with autoregressive errors and their residual processes

Published online by Cambridge University Press:  14 July 2016

R. J. Kulperger
R. J. Kulperger*
Affiliation:
University of Western Ontario
*
∗ Postal address: Department of Statistical and Actuarial Sciences, Faculty of Science, Room 3005 EMSc, The University of Western Ontario, London, Ontario, Canada N6A 5B9.
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Abstract

We consider some linear regression models Y = Σα lfl (z) + X, where X is an autoregressive (AR) process. The residuals estimate the i.i.d. innovations sequence which drives the AR process. We then consider the partial sum process of the residuals and show they converge to Brownian bridges in certain cases. Some remarks are also made on similar processes when differencing is first applied to remove trends. When an AR process is differenced the residual partial sum can be asymptotically a random polynomial.

Keywords

LINEAR REGRESSIONRESIDUALSDIFFERENCINGBROWNIAN MOTIONBROWNIAN BRIDGE

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 668 - 678
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Supported by Natural Sciences and Engineering Research Council of Canada, grant number A5724.

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