Question

part B & C. the results of the unit root test are goven

Homework 7 12.4 The data file oil.dat contains 88 annual observations on the price of oil (in 1967 constant dollars) for the period 1883-1970. (a) Plot the data. Do the data look stationary, or nonstationary? (b) Use a unit root test to demonstrate that the series is stationary (c) What do you conclude about the order of integration of this series?

Answer 1

(b) In general, a p-value of less than 5% means one can reject the null hypothesis that there is a unit root. If the DF_T statistic is more negative than the table value, reject the null hypothesis of a unit root.

a p-value for augmented Dickey-Fuller test is less than 0.01 (1% level of significance) and also t-statistics is negative. This indicates that there is strong evidence against the null hypothesis, thus it needs to be rejected. Hence we conclude that series does not have a unit root.

(c) If one have unit roots in their time series, a series of successive differences, d, can transform the time series into one with stationarity. The differences are denoted by I(d), where d is the order of integration. Non-stationary time series that can be transformed in this way are called series integrated of order k.

As the series does not have a unit root that means series is stationary and has 0 order of integration I(0).