Question 4 (10 marks) Consider the daily stock price of Toyota over the period 3 January 2005 to 22 April 2022, which is denoted by PTM,t. Figure 8 depicts its Autocorrelation Function (ACF). 1. From visual inspection of the ACF in Figure 8, would you consider PTM,t to be a stationary or non-stationary process? Justify your answer. (2 marks) 2. Assume that PTM,t follows a random walk with drift: PTM,t +PTM,t-1+nt, t = 1,2,... with initial value PTM,0 = 0, where nt is a white noise with zero mean and variance o2. Derive E (PTM,t) and V (PTM,t). What do these moments imply about the stationarity of PTM,t? (5 marks) 3. Construct an ADF test to verify whether PTM,t is a stationary or unit root process. Given the results provided in Figure 9 what conclusion do you draw? Provide all steps in your testing procedure. (3 marks) (continued) Question 4 (10 marks) Consider the daily stock price of Toyota over the period 3 January 2005 to 22 April 2022, which is denoted by PTM,t. Figure 8 depicts its Autocorrelation Function (ACF). 1. From visual inspection of the ACF in Figure 8, would you consider PTM,t to be a stationary or non-stationary process? Justify your answer. (2 marks) 2. Assume that PTM,t follows a random walk with drift: PTM,t +PTM,t-1+nt, t = 1,2,... with initial value PTM,0 = 0, where nt is a white noise with zero mean and variance o2. Derive E (PTM,t) and V (PTM,t). What do these moments imply about the stationarity of PTM,t? (5 marks) 3. Construct an ADF test to verify whether PTM,t is a stationary or unit root process. Given the results provided in Figure 9 what conclusion do you draw? Provide all steps in your testing procedure. (3 marks) (continued)