A researcher wants to test the order of integration of some time series data. He decides to use the DF test. He estimates a regression of the form

yt = μ + ψyt−1 + ut and obtains the estimate ˆψ = −0.02 with standard error = 0.31.

(a) What are the null and alternative hypotheses for this test?

(b) Given the data, and a critical value of −2.88, perform the test.

(c) What is the conclusion from this test and what should be the next step?

(d) Why is it not valid to compare the estimated test statistic with the corresponding critical value from a t-distribution, even though the test statistic takes the form of the usual t-ratio?

AppendixLO1