I. Gaussian White Noise Model (8 points, 4 points each) Consider the gaussian white noise (GWN) model rit = Hi + Eith Eit~iid N (0, o?) cov (rit, rit) = ij, cor (rit, rit) = Pij for the monthly simple returns on the Vanguard S&P500 index (VFINX) and Amazon stock (AMZN) using monthly closing price data over the period January, 2014 through January, 2019. The following R output gives the estimates of Hi, Ci, ij and piffor the S&P 500 index (VFINX) and Amazon stock (AMZN) from the 7=60 months of data: > muhat . vals vfinx AMZN 0 . 00913 0. 02997 > sigmahat . vals vfinx AMZN 0 . 0335 0 . 0856 > covhat . vals vfinx, AMZN 0 . 00182 > rhohat . vals vfinx, AMZN 0 . 634 24 month rolling means and sds for VFINX 0.05 0.00 returns 0.05 . . . . . . Rolling mean - - - Rolling sd Monthly returns -0.1024 month rolling means and sds for VFINX 0.05 0.00 returns -0.05 . . . . . . Rolling mean - - - Rolling sd Monthly returns -0.10 2015 2016 2017 2018 2019 Index Figure 1 Rolling estimates for VFINX 24 month rolling means and sds for AMZN 0.2 01 returns 0.0 -0.1 . . . . . . Rolling mean - - - Rolling sd -0.2 Monthly returns 2015 2016 2017 2018 2019 Index Figure 2 Rolling estimates for AMZN 1. The 24-month rolling estimates of p are illustrated in Figure 3 below . The GWN model assumes that p is constant over time. Is this a reasonable assumption? Why or why not? Rolling Correlation b/w VFINX and AMZN 1.0 0.8 0.6 hareturns 0.0 -0.1 . . . . . . Rolling mean Rolling sd -0.2 Monthly returns 2015 2016 2017 2018 2019 Index Figure 2 Rolling estimates for AMZN 1. The 24-month rolling estimates of p are illustrated in Figure 3 below . The GWN model assumes that p is constant over time. Is this a reasonable assumption? Why or why not? Rolling Correlation b/w VFINX and AMZN 1.0 0.8 0.6 rho.hat 0.4 0.2 0.0 2016 2017 2018 2019 Index Figure 3 Rolling correlations between VFINX and AMZN 2. Give Figure 1, Figure 2, and Figure 3, do you think the returns on vfinx and AMZN come from a covariance stationary time series