Note X(t)-X(t-1)=4+W(t)-.75W(t-1)
If, X(t)-X(t-1)=Y(t) then Y(t) is an MA(1) process. so in Arima(p,d,q), p=0,d=1,q=1.
now Y(t)=grad(X(t))
E(Y(t))=4+0+0=4 since E(W(t))=0 for all t
V(Y(t))=. This is because W(t)'s are iid(White noise process are iid processes)
consider the ARIMA model 8. Consider the ARIMA model X,-4 + Xt-1 + W-0.75W,-1, W, ~ WN(0, σ*) a. Identify p, d, and q. Write the corresponding ARMA (p,q) model. b. Find E VX and VarVX 8. Cons...
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.
3. Write the complete model for the flowing: (a) AR(P = 2)d=12 (b) MAQ = 2)d=12 (c) ARMA(P = 1,Q = 2).-12 (d) ARMA(P = 2,Q=0)d=12 (e) ARMA(p = 0,9 = 2) (P = 1,Q = 2)d-12 (f) SARIM A(p = 1, d = 19 = 1) (P = 1, D = 1,Q = 1).-12
2. Consider an ARMA(1,1) process, X4 = 0.5X:-1 +0+ - 0.25a4-1, where az is white noise with zero mean and unit variance. (a) Is the model stationary? Explain your answer briefly. (b) Is the model invertible? Explain your answer briefly. (c) Find the infinite moving-average representation of Xt. Namely, find b; such that X =< 0;&–; j=0 (d) Evaluate the first three lags of the ACF and PACF.
B. Consider the GARCH (1, 1) model Xt-σ.zt, σ -00 + α1XL1 + βισ -1 where Zt are iid N (0, 1) process, ao 0, α120, ai 1 > α1 + β1. Show that 0, A > 0 and 2IV2 t-1't-2 .. B. Consider the GARCH (1, 1) model Xt-σ.zt, σ -00 + α1XL1 + βισ -1 where Zt are iid N (0, 1) process, ao 0, α120, ai 1 > α1 + β1. Show that 0, A > 0...
please help !!!! 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x = n-ı Σ i , and y = n-ı Σ -1 y be the sample means of the x and y variables. Let & and Sy be the corresponding standard deviations. Let sry and rry be the sample covariance and sample correlation respective . Suppose x = 6.2,J = 8 8 2.95, sy4.494, sy 13.05. Part a) What is the sample correlation of the...
2. Points = 26. Consider Market Model: Demand: Supply: Q=a-bP Q=-c+dP (a, b>0) (c,d > 0) 1) Discuss in words the meaning of each equation in the model (3 points); 2) Find the equilibrium levels of P* and Q* (3 points); 3) Draw qualitative conclusions about changes in P* and Q* when each of the parameters change. (Qualitative conclusion shows the direction of change.) Explain economic meaning of these changes. (Total 6 points: 3 points for P*; 3 points for...
Consider Market Model: Demand: Supply: Q= a - bP Q=-c+dP (a, b > 0) (c, d > 0) * 1) Discuss in words the meaning of each equation in the model (3 points); 2) Find the equilibrium levels of P* and Q* (3 points); 3) Draw qualitative conclusions about changes in P* and Q* when each of the parameters change. (Qualitative conclusion shows the direction of change.) Explain economic meaning of these changes. (Total 6 points: 3 points for P*;...
Solve part (d) 6. Consider the eigenvalue problem 2"xy3y Ay 0 y(1)0, y(2)= 0. + 1 < x< 2, (a) Write the problem in Sturm-Liouville form, identifying p, q, and w. (b) Is the problem regular? Explain (c) Is the operator S symmetric? Explain (d) Find all eigenvalues and eigenfunctions. Discuss in light of Theorem 4.3 ln x, 1 < 2, in terms of these (e) Find the orthogonal expansion of f(x) eigenfunctions _ 6. Consider the eigenvalue problem 2"xy3y...
Cauchy. 4. (4 points) Suppose X ~ (a) Find P(X E [0, 8]). (Hint: tan-"(a) = 1Haz.) (b) Find P(3X + 5 € [0, 8]). 1+a²