Squared residuals versus just residuals? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T12:13:19Z http://mathoverflow.net/feeds/question/72227 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72227/squared-residuals-versus-just-residuals Squared residuals versus just residuals? Palace 2011-08-06T05:19:47Z 2011-08-07T01:14:52Z <p>In statistics (in particular time series analysis, like ARCH/GARCH models) I've noticed that residual diagnostics usually look at autocorrelation of residuals and squared residuals. Why both? What does autocorrelation of the squared residuals tell us that is different to just the regular residuals?</p> http://mathoverflow.net/questions/72227/squared-residuals-versus-just-residuals/72256#72256 Answer by Igor Rivin for Squared residuals versus just residuals? Igor Rivin 2011-08-06T18:27:24Z 2011-08-07T01:14:52Z <p>Apparently there are cases when residuals are not auto-correlated, but the square residuals are, and this observation goes back to at least the Engle's 1982 ARCH paper. See </p> <p><a href="http://www.jstor.org/stable/3315329" rel="nofollow">http://www.jstor.org/stable/3315329</a></p> <p>(even if you don't have full access to JSTOR, the first page should be enlightening.)</p> <p><strong>EDIT</strong> The real point is this. Consider a day like August 4, 2011 at the markets. At the end of the day, it was not clear if the next day would be up or down, but it <em>was</em> clear that it would be volatile. So, the square (or the absolute value) of the changes are correlated, while it is not clear that the actual changes are themselves...</p>