Exercise Solution 4.17

The Ljung and Box test statistic


is approximately centrally chi-squared with h degrees of freedom: S ~ χ2(h,0), assuming . Accordingly, a significance level 0.05 non-rejection region for  will be the set of values s less than the 0.95 quantile of S. In this case, h = 3. The 0.95 quantile of a χ2(3,0) distribution is 7.81 (in Microsoft Excel, this can be obtained with formula  =chisq.inv(0.95,3) ). Based on α = 250 and the three sample autocorrelations 0.085, –0.027 and 0.109, test statistic [4.49] is evaluated as 5.02. This is less than 7.81, so the null hypothesis is not rejected at the 0.05 significance level.