Testing Serial Correlation Using the Gauss–Newton Regression

  • Efigénio RebeloEmail author
  • Patrícia Oom do Valle
  • Rui Nunes
Part of the Studies in Theoretical and Applied Statistics book series (STAS)


This paper proposes two types of autocorrelation tests based on a methodology that uses an auxiliary regression, named Gauss–Newton regression. All tests are derived considering that the regression function contains contemporary values of endogenous variables, situation in which the model is estimated using the nonlinear instrumental variables method. The first type of test intends to identify the presence of serial correlation, whether genuine or not. The second type of test is proposed to distinguish the genuine serial correlation from the non-genuine serial correlation, being the latter an evidence of misspecification. This study also shows that this second type of test, called the “Common Factor Restrictions” test, can be deduced as a χ 2 test or as a t test.


Regression Function Serial Correlation Consistent Estimate Restricted Version Instrumental Variable Method 
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Supported by FCT under the Annual Financial Support Program for Research Units granted to CEC and CMUP.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Efigénio Rebelo
    • 1
    Email author
  • Patrícia Oom do Valle
    • 1
  • Rui Nunes
    • 1
  1. 1.Research Centre for Spatial and Organizational Dynamics (CIEO)University of AlgarveAlgarvePortugal

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