Skip to main content

Table 3 The SARMA \((2,0)\times (0,3)_{12}\) model was fitted to the monthly difference of the differenced federal reserve board production index data

From: Portmanteau test statistics for seasonal serial correlation in time series models

Test

\(m=10\)

\(m=15\)

\(m=20\)

\(s=12\)

\(s=1\)

\(s=12\)

\(s=1\)

\(s=12\)

\(s=1\)

\(Q_{m}(s)\)

0.822

0.114

0.381

0.030

0.574

0.069

\(\hat{Q}_{m}(s)\)

0.744

0.107

0.087

0.024

0.093

0.055

\(\tilde{Q}_{m}(s)\)

0.824

0.097

0.676

0.033

0.596

0.058

\(\mathfrak {D}_{m}(s)\)

0.623

0.057

0.520

0.076

0.570

0.054

  1. The residuals of the fitted model are tested at the seasonal and nonseasonal lags using the portmanteau test statistics \(Q_{m}(s),\hat{Q}_{m}(s),\tilde{Q}_{m}(s)\), and \(\mathfrak {D}_{m}(s)\) approximations, where \(s=1,12\) (for nonseasonal and seasonal respectively) and \(m=10,15,\) and 20