The degrees of freedom of the asymptotic distribution of the Ljung-Box test statistic is the number of auto correlations included minus the number of parameters estimates. You will find an explanation in any good time series test (e.g. Brockwell and Davis (2006), Shumway and Stoffer (2006 2011(?)), Tsay (2010) ). Remember this result is only asymptotic and therefore is only approximate. Some software packages therefore do not include the adjustment to the degrees of freedom. There are no universally accepted rules as to the number of lags that should be included in the autocorrelation function. Best Regards John 2011/5/23 Sam Sam <dear.sam(a)livemail.tw&gt;: -- John C Frain Economics Department Trinity College Dublin Dublin 2 Ireland www.tcd.ie/Economics/staff/frainj/home.html mailto:frainj@tcd.ie mailto:frainj@gmail.com