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To overcome the limitations of the DW test, Breusch (1978) and Godfrey (1978) introduced a Lagrange multiplier (LM) test which is a more general test for rth order autocorrelation:
The null and alternative hypotheses for the LM test are:
As showed by Hatemi (2004) the performance and order of autocorrelation of the LM test is satisfactory when used in a different sample size.
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