2. AR1 process (5 + 10 + 10 + 5 + 10 pts) Define the time-series {Yt , t = 1, 2, . . . } as follows: Yt = ( e1 t = 1 ?Yt?1 + et t > 1 (1) where {et , t = 1, 2, . . . } is white noise with mean 0 and variance ? 2 , and ? is a constant with |?|

1. Calculate the mean function of {Yt}

2. Calculate the variance function of {Yt}. Is the process weakly stationary?

3. Show that Corr(Yt ,Yt?h) = ? h qVar(Yt?h) Var(Yt) , h > 0. 4. What are Var(Yt) and Corr(Yt ,Yt?h) as t ? ?? (Note that the dependence on t disappears!) 5. Suppose we alter the initial condition to Y1 = ? e1 (1?? 2) . Show that this process is weakly stationary

2. AR process (5 + 10 + 10 + 5 + 10 pts) Define the time-series { Yt, t = 1,2, ...} as follows: E1 t = 1 Y+ = (1) OYtite t>1 where {et,t = 1,2,...} is white noise with mean 0 and variance o2, and 0 is a constant with 101 O. 4. What are Var(Yt) and Corr(Yt, Yt-h) as t - co? (Note that the dependence on t disappears!) 5. Suppose we alter the initial condition to Y1 = E1 V ( 1-02 ) Show that this process is weakly stationary