Finally, Dennehy would like to confirm that nonstationarity is not a problem. To test for this he conducts Dickey–Fuller tests for a unit root on each of the time series. The results are reported in Exhibit 2.
EXHIBIT 2
RESULTS OF THE DICKEY-FULLER TESTS
| Time Series | Value of the Test Statistic | Standard Error | t-Statistic | Significance of t |
|---|---|---|---|---|
| Defective assemblies per hour | 0.0036 | 0.0023 | 1.591 | 0.1123 |
| Outside air temperature | –0.423 | 0.0724 | –5.846 | 0 |
| Assembly line speed | –0.586 | 0.043 | –13.510 | 0 |
Q. Assuming a 5% level of significance, the most appropriate conclusion that can be drawn from the Dickey–Fuller results reported in Exhibit 2 is that the:
- test for a unit root is inconclusive for the dependent variable.
- independent variables exhibit unit roots but the dependent variable does not.
- dependent variable exhibits a unit root but the independent variables do not.
Solution
C is correct. The Dickey–Fuller test uses the following type of regression:
xt − xt−1 = b0 + g1xt−1 + εt, E(εt) = 0
The null hypothesis is H0: g1 = 0 versus the alternative hypothesis Ha: g1 < 0 (a one-tail test). If g1 = 0, the time series has a unit root and is nonstationary. Thus, if the null hypothesis fails to be rejected, then the possibility exists that the time series has a unit root and is nonstationary.
Based on the t ratios and their significance levels in Exhibit 2, the null hypothesis that the coefficient is zero is rejected for both outside air temperature and assembly line speed (i.e., the independent variables). But the null hypothesis is not rejected for the dependent variable, defective assemblies per hour.
此题选项涉及因变量，我不记得如何判断因变量是否有单位根了，烦请解释一下，谢谢！
EXHIBIT 2
RESULTS OF THE DICKEY-FULLER TESTS
EXHIBIT 2
RESULTS OF THE DICKEY-FULLER TESTS
