Question 5 a. Many time series used in finance are described as non-stationary series. What do we mean by non-stationary? Why is it important to test for non-stationarity and account for it in estimation? [4 marks] b. Three forms of standard Dickey-Fuller test are given below: A. Ayt = pyt-1 + ut B. Ayt = a+pyt-1 + Ut C. Ayt = a + Bt + pyt-1 + ut Which of these forms would you use to test for non-stationarity in each of the following variables and why? i. Stock prices ii. Stock returns iii. The residuals of an Engle-Granger test [2+2+2=6 marks] Consider the following data generating process for a series yt: y, = 4 +1.5y +u, c. What most accurately describes the process for yt? How would you work with this model for yt? [4 marks] d. What difficulties can arise when applying and interpreting Dickey-Fuller tests? Describe in detail another test which could be applied to test for non-stationarity. [3+3 = 6 marks] [Total of Question 5 = 20 marks] Question 5 a. Many time series used in finance are described as non-stationary series. What do we mean by non-stationary? Why is it important to test for non-stationarity and account for it in estimation? [4 marks] b. Three forms of standard Dickey-Fuller test are given below: A. Ayt = pyt-1 + ut B. Ayt = a+pyt-1 + Ut C. Ayt = a + Bt + pyt-1 + ut Which of these forms would you use to test for non-stationarity in each of the following variables and why? i. Stock prices ii. Stock returns iii. The residuals of an Engle-Granger test [2+2+2=6 marks] Consider the following data generating process for a series yt: y, = 4 +1.5y +u, c. What most accurately describes the process for yt? How would you work with this model for yt? [4 marks] d. What difficulties can arise when applying and interpreting Dickey-Fuller tests? Describe in detail another test which could be applied to test for non-stationarity. [3+3 = 6 marks] [Total of Question 5 = 20 marks]