Recall that the MA(q) process is defined as:
= where {} is a white noise process with variance <
a) Construct an expression for
b) Construct an expression for
c) Construct an expression for the autocovariance and autocorrelation functions.
Recall that the MA(q) process is defined as: = where {} is a white noise...
Consider the random walk model where {} is a white noise process with variance a) How many parameters does this model have? b) calculate and c) Compute for d) Is this model weakly stationary? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagevar(yt) We were unable to transcribe this imageWe were unable to transcribe this image
Recall that a time series {εt} is called a white noise process if i. E[εt] = 0 t ; ii. Cov(εs, εt) = 0 s ≠ t ; iii. Var(εt) = σ2 < ∞ Construct the autocorrelation function f(h), h=0,-+1,-+2,… for the white noise process.
The time series {} is said to be an AR(2) process if , where {} is a white noise process with variance < a) For what values of is the process weakly stationary? b) Select in the range where the process is weakly stationary and plot the autocorrelation function for the chosen We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
2. Let (et) be a zero mean white noise process with variance 1. Suppose that the observed process is h ft + Xt where β is an unknown constant, and Xt-et- Explain why {X.) is stationary. Find its mean function μχ and autocorrelation function p for lk0,1,.. a. b. Show that {Yt3 is not stationary. C. Explain why w. = ▽h = h-K-1 is stationary. d. Calculate Var(Yt) Vt and Var(W) Vt . (Recall: Var(X+c)-Var(X) when c is a constant.)...
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 process Y.-μ + et-o, et-1-912 et-12, where {ed denotes a white-noise process with mean 0 and variance σ? > 0. Assume that et ls independent of Yt-1, Yt-2, Find the autocorrelation function for (Yt).
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the exit process Y (t) knowing that We were unable to transcribe this imager. h2 (t)dt = 1. r. h2 (t)dt = 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...
: Assume Yt is a time series process and Et is a white noise process with mean zero and constant variance. (a). Write an equation for AR(4) process. (b). Write an equation for AR(5) process. (c). Write an equation for MA(3) process. (d). Write down an equation for MA(2) process. (e). Write an equation for ARMA (4,2) process. (f). Do more research and write an equation for ARIMA (4,0,2) proce
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,...