Question

An analyst considers to test the order of integration of some time series data. She decides to use the DF test. She estimates a regression of the form 〖Δy〗_t=μ+ψy_(t-1)+u_t and obtains the estimate ψ ̂=-0.03 with standard error = 0.32. 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?

Answer 1

The given time series model is

a) The null and alternative hypotheses for DF test are

b) Given the data, a critical value of -2.88.

Test statistic value is

c) The test statistics value is compared to the relevant critical value for the DF Test. Here, we see that the test statistic is greater than the critical value, we fail to reject the null hypothesis and conclude that time series is not stationary, i.e., unit root is present.

So, We make a difference and get a stationary series.

d) Since, it is not possible to use a standard t-distribution to provide critical values for this test because this test statistic has a specific distribution simply known as the DF distribution.