The RATS Software Forum

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Campbell, Lo and MacKinlay has a rather long chapter on tests of the RW hypothesis, starting with the most restrictive interpretation (i.i.d. mean zero increments), loosening it to simply independent, and finally to uncorrelated. You might want to take a look at that. (Someone else might be able to suggest a more recent reference). If you want to do a run test, you can use the RUNTEST procedure. You can also check out the BDINDTESTS procedure, which does a whole set of non-parametric tests for independence.