Question 4. (20 points) Consider the following GARCH (1,1) model yt=+ut,utN(0,t2)t2=0+1ut12+t12 a) If yt is a daily stock return series, what range of values are likely for the coefficients ,0,1 and ? b) Suppose now that the researcher had estimated the above GARCH model for a series of returns on a stock index and obtained the following parameter estimates: =0.23,0=0.12,=0.38,1=0.12. What is the unconditional variance of yt ? Briefly prove the formula. c) If the data are available up to time T, produce one-, two-step ahead forecasts for conditional variance of yt. Question 4. (20 points) Consider the following GARCH (1,1) model yt=+ut,utN(0,t2)t2=0+1ut12+t12 a) If yt is a daily stock return series, what range of values are likely for the coefficients ,0,1 and ? b) Suppose now that the researcher had estimated the above GARCH model for a series of returns on a stock index and obtained the following parameter estimates: =0.23,0=0.12,=0.38,1=0.12. What is the unconditional variance of yt ? Briefly prove the formula. c) If the data are available up to time T, produce one-, two-step ahead forecasts for conditional variance of yt