Problem 3 Express growth rates for xt in terms of growth rates of Yt and zt....
Zt is a function of Xt, Y4 and Ut. Express the growth rate of Zų as a function of growth rates of Xt, Yt and Ut for the following cases (no need to show the intermediate steps): Question 4.1 [5 points Zt = X Y3 Question 4.2 (5 points) Zt Question 4.3 [5 points) Z4 = VX+Y4
Problem 3 Consider a random walk on the integers. Suppose we start from 0, and at each step, we either go left or right with probability 1/2, ie, Xo--0, and Xt+1 Xt+Zt, where Zt-1 with probability 1/2, and Zt1 with probability 1/2. What is the probability distribution of XT? What is E(X) and Var(XT)? Problem 3 Consider a random walk on the integers. Suppose we start from 0, and at each step, we either go left or right with probability...
Suppose Zt = 2 + Xt -2Xt-1+Xt-2, where {Xt} is zero-mean stationary series with autocovariance function. Calculate the autocovariance of Zt
Find the spectral density of Xt =−0.7Xt−1+Zt −0.3Zt−1+0.7Zt−2, {Zt}~IID(0,2).
Consider the following AR(2) model: Xt – Xt–1 + + X4-2 = Zt, Z4 ~ WN(0,1). (a) Show that X+ is causal. (b) Find the first four coefficients (VO, ..., 43) of the MA(0) representation of Xt. (c) Find the pacf at lag 3, 233, of the AR(2) model.
Consider the model defined by, Yt = BO + B1 Yt-1 + B2 Xt + Ut. Compute the long-run coefficients (2 decimals) for the model: Short-Run Long-Run BO 1.38 B1 0.60 B2 -5.26
For the system in problem below, find the output yt if the input xt=ut, and y0-=4, y'0=0. y''t+10y't+16yt=3x(t)
For the following system of first order difference equations xt+1=-xt-2yt +24 yt+1= -2xt+2yt+9 1) Present the system in matrix form. (2) Find the equilibrium vector. (3) Find the eigenvalues and eigenvectors for this system. (4) Find the general solution. (5) Plot the phase diagram.
Find the spectral density functions of the following MA process: Xt = Zt + 0.5Zt−1 − 0.3Zt−2
Consider the process where B is a backwards shift operator so that BXt-Xt-i and the {Zt) are assumed to be independent random errors. (a) [2 marks] Identify what kind of nonseasonal ARIMA(p,d,q) process this is; that is give the parameters (p,d,q) and give the abbreviated name for this particular process. (b) [3 marks] (i) Is this particular process stationary? Explain. (ii) Is this process invertible? Why? Consider the process where B is a backwards shift operator so that BXt-Xt-i and...