Because nonstationarity or heteroskedasticity would negatively affect use of the AR(1) model, Reyes asks the students to test for the presence of each. Results of the unit root test for nonstationarity and of a test for the presence of heteroskedasticity are reported in Exhibit 5.
Exhibit 5
Unit Root Test for Nonstationarity and the Test for
Heteroskedasticity
Unit root test statistic – 18.7402
Unit root test critical value at the –2.89
5% level of significance
Heteroskedasticity test statistic 2.016733
Heteroskedasticity test critical value at
the 5% level of significance 1.96
Based on the results reported in Exhibit 5, the AR(1) model is best described as having:
1)reliable standard errors.
2)heteroskedasticity in the error term variance.
3)a unit root.
The correct answer is 2)
Explanation :
Because the unit root test statistic (–18.7402) is smaller than the critical value (–2.89), the AR(1) model does not exhibit a unit root. The test for heteroskedasticity, however, suggests that the error term variances are heteroskedastic. The heteroskedasticity test statistic (2.016733) is greater than the critical value (1.96). A more sophisticated approach, such as generalized least squares, is needed.
My question is because the unit root test statistic (–18.7402) is smaller than the critical value (–2.89), should we reject the hypothesis and exhibit a unit root instead of the explanation above? I am just confused here. Is it because it is a one tail-test ? We need to have a value over critical value as opposed to be less than it?
Thanks,