1. Assume that the cumulative return Rt for stock A follows a random walk Rt = r1 + r2 + + rt , where each ri , 1 i t follows a normal distribution with mean 0 and variance 0.05, and they are independent. What is the variance for R5 . 2. Suppose we have the following Box test result on a time series. What conclusion can we make about this time series and why?(3 pts) Box.test(Residuals,lag=20) Box-Pierce test data: Residuals X-squared = 69.453, df = 20, p-value = 2.237e-07 3. Assume we have a series Yt = 2(wt wt1 ), where wt are white noises with distribution N (0, 2 ), t = 1, 2, . Compute E(Yt ) and V AR(Yt ). Is this series weakly stationary? why? Hint: V AR(Yt ) = V AR(2 (wt wt1 )) = 22 V AR(wt wt1 ) since 2 is a constant. Now V AR(wt wt1 ) = V AR(wt ) + V AR(wt1 ) since wT and wt1 are uncorrelated. 4. The random walk process Xt = w1 + w2 + + wt where wt N (0, 2 ). Hint: we did the more general version in class. what are E(Xt ) and V (Xt )? What is COV (X1 , X2 )? What is COV (w3 , X1 )? 1