 Hi,

I would like to ask/clarify how should degrees of freedom (and p-values) for the Ljung-Box Q-statistics in arma and garch models be computed. The reason for the question is that I have encountered two different approaches. Let us say we have an arma(p,q) garch(m,n) model. The two approaches are as follows:

1) In R and fArma and fGarch packages, the arma and garch orders are disregarded in the computation of degrees of freedom for the Ljung-Box (LB) Q-statistics. In other words, regardless of p, q, m and n, the LB Q-statistic computed from the first x autocorrelations of (squared) standardised residuals has x degrees of freedom. Given the statistic and degrees of freedom, the corresponding p-value is computed.

2) In EViews, TSP and other statistical software, the LB Q-statistic computed from the first x autocorrelations of standardised residuals has (x - (p+q)) degrees of freedom. Degrees of freedom and p-values are not computed for the first (p+q) LB Q-statistics. A similar method is applied to squared standardised residuals: the LB Q-statistic computed from the first x autocorrelations
of squared standardised residuals has (x - (m+n)) degrees of freedom.
Degrees of freedom and p-values are not computed for the first (m+n) LB
Q-statistics.

I think the second approach is better because the first (p+q) orders in standardised residuals and the first (m+n) orders in squared standardised residuals should not exhibit any pattern and higher orders should be checked for any remaining arma and garch structures. Am I right or wrong?

Thanks for answers and suggestions.

Best regards

Michal Miklovic





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