2. [30 marks] The values of a stock index over four days are given in the table below. Day Index 0 20436 1 20794 2 21059 3 20751 The volatility on Day 2 is estimated with 2 = \u1l. (a) Estimate the daily volatility z on Day 3 using the EWMA model with = 0.95. (b) Estimate the daily volatility 3 on Day 3 using the GARCH(1,1) model with a= 0.01, B = 0.95, y = 0.04, and oL = 0.01. (c) Calculate the log-likelihood for part (b). (d) Estimate the daily volatility z on Day 3 using the GARCH(1,1) model with a = 0.02, B = 0.96, y = 0.02, and ol 0.02. (e) Calculate the log-likelihood for part (d). (f) Which set of parameters, part (b) or (d), is better? = 2. [30 marks] The values of a stock index over four days are given in the table below. Day Index 0 20436 1 20794 2 21059 3 20751 The volatility on Day 2 is estimated with 2 = \u1l. (a) Estimate the daily volatility z on Day 3 using the EWMA model with = 0.95. (b) Estimate the daily volatility 3 on Day 3 using the GARCH(1,1) model with a= 0.01, B = 0.95, y = 0.04, and oL = 0.01. (c) Calculate the log-likelihood for part (b). (d) Estimate the daily volatility z on Day 3 using the GARCH(1,1) model with a = 0.02, B = 0.96, y = 0.02, and ol 0.02. (e) Calculate the log-likelihood for part (d). (f) Which set of parameters, part (b) or (d), is better? =