For the United States, There Is Somewhat Conflicting Evidence Whether

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?