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 delta yt = mu + si yt-1 + mut
and obtains the estimate ˆ? = -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?

a) H0: u = presence of a unit root

   HA: u ≠ presence of a unit root  ( i.e. stationary series )

b) t stat = -0.064

c) We will reject the Null hypothesis and the next step will be to accept the alternative hypothesis

d) It is not valid to compare the estimated t stat with the corresponding critical value because a random walk is non-stationary while the difference is stationary because it is white noise

Explanation:

a) stating the null and alternative hypothesis

H0: u = presence of a unit root

HA: u ≠ presence of a unit root  ( i.e. stationary series )

b) performing the test

critical value = -2.88

T stat = coefficient / std error

          = -0.02 / 0.31  = -0.064

c) From the test, the value of T stat > critical value we will reject the Null hypothesis hence the next step will be to accept the alternative hypothesis

d) It is not valid to compare the estimated t stat with the corresponding critical value because a random walk is non-stationary while the difference is stationary because it is white noise