. Consider a moving average MA(2) model: y(t) = e(t)+b, e(t-1) +b,elt - 2) Assume that...
1. Consider a moving average MA(2) model: y(t) = e(t) +belt-1) + b,elt-2) Assume that the noise e(t) has is i.i.d. with variance = 1. (a) Compute the autocorrelation process r(k) for y(t). (b) Compute the PSD of y(t). (Hint: 12.4 +e=24 = 2 cos(24)) (c) Plot the spectral density from part (b) for at least FOUR different combinations of (b1,b2), where b and b take either positive or negative values. (d) Comment on where the peaks of the PSD...
. Consider a moving average MA(2) model: y(t) = e(t)+b, e(t-1) +b,elt - 2) Assume that the noise e(t) has is i.i.d. with variance o = 1. (b) Compute the PSD of y(t). (Hint: e24 +e 1214 = 2 cos(274))
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,...
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?
True or false? You do not have to provide explanations. (a) Any moving average (MA) process is covariance stationary. (b) Any autoregressive (AR) process is invertible. (c) The autocorrelation function of an MA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off. (d) Suppose yt is a general linear process. The optimal 2-step-ahead prediction error follows MA(2) process. (e) Any autoregressive moving average (ARMA) process is invertible because any moving average (MA) process is invertible. (f) The...
Convert the following auto-regressive (AR) model into a moving average (MA) model: Y, = 1 + 0.19-1 +ęt
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the simple moving average model Xt = 0.02 + Wt − 0.4Wt−1, where Wt is a sequence of i.i.d. normal random variables with mean zero and variance 4. What is the mean of Xt? What is the variance of Xt. Show working
what is the correct answer? please provide the calculation . Consider the following MA(1) model with the errors Et having having zero mean, unit variance and being serially uncorrelated. Yt = 0.2 + E +0.5&t-1 The value of the autocorrelation coefficient at lag 1 is: 0.5 0.25 0 0.4