Consider the \(\operatorname{ARDL}(p, q)\) equation

and the data in the file usmacro. For \(p=2\) and \(q=1\), results from the LM test for serially correlated errors were reported in Table 9.6 for \(\operatorname{AR}(k)\) or \(\operatorname{MA}(k)\) alternatives with \(k=1,2,3,4\). The \(\chi^{2}=T \times R^{2}\) version of the test, with missing initial values for \(\hat{e}_{t}\) set to zero, was used to obtain those results. Considering again the model with \(p=2\) and \(q=1\), compare the results in Table 9.6 with results from the following alternative versions of the LM test.

1. The \(\chi^{2}=T \times R^{2}\) version of the test, with missing initial values for \(\hat{e}_{t}\) dropped.

2. The \(F\)-test for the joint significance of lags of \(\hat{e}_{t}\), with missing initial values for \(\hat{e}_{t}\) dropped.

3. The \(F\)-test for the joint significance of lags of \(\hat{e}_{t}\), with missing initial values for \(\hat{e}_{t}\) set to zero.

Transcribed Image Text:

U = 8 + 0 U - + + 0U +8 G1 + 1-1 +8G-q+e