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1. Consider the following autoregressive process 2+ = 4.0 + 0.8 2t-1 + Ut, where E...
help wih these question please 3. Consider the following autoregressive process Yt = Bo + B1yt-1...
help wih these question please
3. Consider the following autoregressive process Yt = Bo + B1yt-1 + B2Yt-2 + Ut, where E (UtYt-1, Yt-2, ...) = 0. You obtained the following parameter estimates: Bo= -0.2, B1 = 0.4 and B2 = -0.1. Furthermore, you have the following observations: 419 = -0.2 and Y20 = 0.3. What is the estimate for E Y 22 y 20,419)? (a) -0.3333 (b) -0.06 (C) 0.3 (d) -0.2857 (e) -0.254 4. You have estimated the...
a) Consider the following moving average process, MA(2):
a) Consider the following moving average process, MA(2): Yt = ut + α1ut-1 + α2ut-2 where ut is a white noise process, with E(ut)=0, var(ut)=σ2 and cov(ut,us)=0 . Derive the mean, E(Yt), the variance, var(Yt), and the covariances cov( Yt,Yt+1 ) and cov(Yt,Yt+2 ), of this process. b) Give a definition of a (covariance) stationary time series process. Is the MA(2) process (covariance) stationary?
Consider the following AR(1) model: 1. a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. the following random 2. Consider walk...
Consider the following AR(1) model: 1. a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. the following random 2. Consider walk model: yeBo yt-1 +ut, t-0,1,..,T a. Show that yt-3βο + yt-3 + ut + ut-1 + ut-2. b. Suppose that 0-0, show that y.-t βο +4 + ut-1 + + u! c. Suppose that that yo -0, and ut for all t are ii.d. with mean 0 and variance...
2. Consider a following time series process Yt = 1.5Yt−1 −0.5Yt−2 +εt a) Rewrite this process...
2. Consider a following time series process Yt = 1.5Yt−1 −0.5Yt−2 +εt a) Rewrite this process in lag polynomial form. b) Is this process invertible? Is this process covariance stationary? c) Difference this process once and show that ΔYt = Yt −Yt−1 is covariance stationary.
Consider the following assumptions: 1. ?? = ?(? + ??) (data generating process) 2. E(?? )...
Consider the following assumptions: 1. ?? = ?(? + ??) (data generating process) 2. E(?? ) = 0 for all 3. Var(?? ) = ? 2 for all i 4. Cov(?? , ?? ) for ? ≠ ? 5. ?? ∼ ?????? And suppose you’re interested in generating an estimate for ?. a. What is the expected value of the sample mean estimator, ?̂= 1 ? ∑?? , under these assumptions? Is ?̂an unbiased estimator for ?? Show all work...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of {X) and then substitute t = 20. (b) (3 points) Calculate Var(X20) Question 2 continues on the next page... Page 4 of 12 c)(4 points) Consider the first differences of the time series above, that is Is {%) a weakly stationary process. Prove...
Consider the following network with the initial inputs and outputs i-0.8, irl, i,-0.9 with 0,-01-1 0.3 0.3 0.2 2 0. 0.9...
Consider the following network with the initial inputs and outputs i-0.8, irl, i,-0.9 with 0,-01-1 0.3 0.3 0.2 2 0. 0.9 (04 orm 0. 0.1 2. (Please use matlab) Suppose for above problem, the new inputs and the outputs are as follow: i,-12. 12-3, i,-8 and doー9, di How do you solve the problem with appropriate scaling of the inputs and outputs data sets.
Consider the following network with the initial inputs and outputs i-0.8, irl, i,-0.9 with 0,-01-1 0.3...
2. (a) Consider the following process: where {Z) is a white noise process with unit variance. [1 ...
2. (a) Consider the following process: where {Z) is a white noise process with unit variance. [1 mark] ii. Find the infinite moving average representation of X,i.e., find the scquence [6 marks] i. Explain why the process is stationary. (6) such that Xt = Σ b,2-j. iii. Calculate the mean and the autocovariance "Yo, γι and 72 of the process. 7 marks iv. Given 40 = 0.1 and Xo = 1.8, find the 2-step ahead forecast of the time series...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
help wih these question please
3. Consider the following autoregressive process Yt = Bo + B1yt-1 + B2Yt-2 + Ut, where E (UtYt-1, Yt-2, ...) = 0. You obtained the following parameter estimates: Bo= -0.2, B1 = 0.4 and B2 = -0.1. Furthermore, you have the following observations: 419 = -0.2 and Y20 = 0.3. What is the estimate for E Y 22 y 20,419)? (a) -0.3333 (b) -0.06 (C) 0.3 (d) -0.2857 (e) -0.254 4. You have estimated the...
Consider the following AR(1) model: 1. a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. the following random 2. Consider walk model: yeBo yt-1 +ut, t-0,1,..,T a. Show that yt-3βο + yt-3 + ut + ut-1 + ut-2. b. Suppose that 0-0, show that y.-t βο +4 + ut-1 + + u! c. Suppose that that yo -0, and ut for all t are ii.d. with mean 0 and variance...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of {X) and then substitute t = 20. (b) (3 points) Calculate Var(X20) Question 2 continues on the next page... Page 4 of 12 c)(4 points) Consider the first differences of the time series above, that is Is {%) a weakly stationary process. Prove...
Consider the following network with the initial inputs and outputs i-0.8, irl, i,-0.9 with 0,-01-1 0.3 0.3 0.2 2 0. 0.9 (04 orm 0. 0.1 2. (Please use matlab) Suppose for above problem, the new inputs and the outputs are as follow: i,-12. 12-3, i,-8 and doー9, di How do you solve the problem with appropriate scaling of the inputs and outputs data sets.
Consider the following network with the initial inputs and outputs i-0.8, irl, i,-0.9 with 0,-01-1 0.3...
2. (a) Consider the following process: where {Z) is a white noise process with unit variance. [1 mark] ii. Find the infinite moving average representation of X,i.e., find the scquence [6 marks] i. Explain why the process is stationary. (6) such that Xt = Σ b,2-j. iii. Calculate the mean and the autocovariance "Yo, γι and 72 of the process. 7 marks iv. Given 40 = 0.1 and Xo = 1.8, find the 2-step ahead forecast of the time series...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
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