You obtain the following estimates for an AR(2) model of some returns data
yt = 0.803yt−1 + 0.682yt−2 + ut
Where ut is a white noise error process. By examining the characteristic equation, check the estimated model for stationarity.
You obtain the following estimates for an AR(2) model of some returns data yt = 0.803yt−1...
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
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...
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 model 1. Consider the following AR(1) model: a. Explain why this dynamic model violates TS'3 ZCM assumption made for the unbiasedness of the FDL model estimators. b. Show that 1 t-2 2. Consider the following random walk model: ytBo yt-1 +ut, t 0,1,...,T Show that ye 3o yt-3 + ut + Ut-1 +t-2 Suppose that yo - 0, show that yt - tPo + ut + ut-1++u, Suppose that that yo -0, and ut for all t...
3. Suppose Δ1t follows the AR (1) model ΔΥ-30 + λίΔΙǐ-it . Show that Yt follows AR(2) model Derive the AR (2) coefficients for y, as a function of Ao and λι 3. Suppose Δ1t follows the AR (1) model ΔΥ-30 + λίΔΙǐ-it . Show that Yt follows AR(2) model Derive the AR (2) coefficients for y, as a function of Ao and λι
Thank you. I. Derive the error correction model for a model of the type yt-A-+ ßiVt-1 + β2zı + ut-Show all your steps
1. [30 pts! Let Yǐ follow a moving average process of order 1 (ie, MA(1): where e is a white noise process with N(0,1). Suppose that you estimate the model using STATA. You obtain ê-1, ê-0.5 and ớ2-1. You also know e,-2 and E1-1-3. (a) Obtain the unconditional mean and variance of Y (b) Obtain Cor(Y, Yi-1). (c) Obtain the autocorrelation of order 1 for Y 1. [30 pts! Let Yǐ follow a moving average process of order 1 (ie,...
Consider the model, Yt = Bo + B1 X1,1+B1 X2,t + Ut, and this is estimated using OLS with 350 observations. You run some tests with the following results: DWH fails to reject, BG fails to reject, and White test rejects. Select the combination of approaches for the most appropriate estimation of the coefficients. A. Use 2 SLS B. Heteroskedastic correction using X2,t only. c. Use Newey-West HAC. D. Use OLS. Heteroskedastic correction using X1,t only. F. Use White's heteroskedastic-consistent...
4. Consider the ARMA (2, 3) process, I( 0.1%-1 +0.12%-2 + Ze + 0.3Zn-1-0.045-2-0.012Zt-3, where fZ) is a white noise process with unit variance. It is known that the above process is overestimated [4 marks (b) Hence, determine the stationarity and invertibility of the process. [4 marks (c) Find the first three lags of the autocorrelation function (ACF) for the process. [12 marks) (5 marks] (a) Suggest a parsimonious model for the above process. (d) Find the first three lags...