For the United States, there is somewhat conflicting evidence whether or not the inflation rate has a unit autoregressive root

For example, for the sample period 1962:I to 1999:IV using the ADF statistic, you cannot reject at the 5% significance level that inflation contains a stochastic trend. However the null hypothesis can be rejected at the 10% significance level. The DF-GLS test rejects the null hypothesis at the five percent level. This result turns out to be sensitive to the number of lags chosen and the sample period.
(a) Somewhat intrigued by these findings, you decide to repeat the exercise using Canadian data. Letting the AIC choose the lag length of the ADF regression, which turns out to be three, the ADF statistic is
(-1.91). What is your decision regarding the null hypothesis?
(b) You also calculate the DF-GLS statistic, which turns out to be (-1.23). Can you reject the null hypothesis in this case?
(c) Is it possible for the two test statistics to yield different answers and if so, why?
What will be an ideal response?

Answer:
(a) For the Canadian data, the null hypothesis cannot be rejected even at the 10% significance level. Hence for the chosen sample period and lag length, the Canadian inflation rate seems to have a stochastic trend.
(b) The critical value for the DF-GLS statistic is (-1.62) at the 10% significance level. Hence the DF-GLS test comes to the same conclusion as the test based on the ADF statistic: there is evidence of a stochastic trend.
(c) The two test statistics can come to different conclusion, although this is not the case with the Canadian inflation rate. The reason is that the DF-GLS test has more power.