i need help in 1.2 and 1.3 they both are related , In 1.3 you can read it off from 1.2 as the equations from 1.2 is needed in 1.3.

1.2 Random walks 1. Consider the simple random walk (e: is a stationary white noise process) y: = Lit1 + 61: Using back substitution (start with yl = yo + 61), rewrite the previous equation so that y; is a function of yo and of the error term. 2. Consider the random walk with drift {ex is a stationary white noise process) y: =0 +yt1'l'5t Using back substitution (start with 91 = [30 + yo + 81), rewrite the previous equation so that yt is a function of ya, a time trend and of the error term. 0 Consider the stochastic trend model yn=o+it+m with m dened as a simple random walk m = m_1 + e; (e! is a stationary white noise process). Show that this model can be written as ye =51 +yt1+Bt 3. The stochastic trend model (random walk with drift) is given by yt=50+31t+m with 113 dened as a simple random walk 1}: = nhl + at. The deterministic trend model is given by yt=5o+5it+8a where 8: is a stationary white noise process. Explain the difference between these two types of trend model. Will they give similar forecasts? Why? Which one will generate forecasts with more volatility? 1 .3 Stationarity When a variable yt is stationary we require that the mean and variance are constant {do not vary in time). You will need to take the expectation of y, Etyg, to compute the mean and the variance of 9:, Varyt). 0 Using the equation you obtained above in [1] show that yt is nonstationary. Show your steps and any assumptions you have used. 0 Using the equation you obtained above in [2] show that gt is nonstationary. Show your steps and any assumptions you have used