# Exercise Solution 4.17

The Ljung and Box test statistic

[4.49]

is approximately centrally chi-squared with *h* degrees of freedom: *S* ~ χ^{2}(*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 χ^{2}(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.