1. Suppose that Y, follows the Moving Average process of order 1 (MA(1)) model Y₁ = Et - 0&t-1, where &t is i.i.d. with E(E+) = 0 andVar(t) = 0².a) Compute the mean and variance of Yb) Compute the first two autocovariances of Yc) Compute the first two autocorrelations of Y

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Answered: 1. Suppose that Y, follows the Moving…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that Yt follows the Moving Average process of order 1 (MA(1)) model Yt=ϵt−θϵt−1, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=σϵ2 . a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations of
1. Suppose that Yt follows the Moving Average process of order 1 (MA(1)) model Yt=ϵt−θϵt−1, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=σϵ2 . a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations of Yt
If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.
Suppose that Yt follows the stationary AR(1) model Yt = 2.5 + 0.7Yt - 1 + ut,where ut is i.i.d. with E(ut) = 0 and var1ut2 = 9.a. Compute the mean and variance of Yt. b. Compute the first two autocovariances of Yt. c. Compute the first two autocorrelations of Yt.d. Suppose that YT = 102.3. Compute YT+1|T = E(YT+1 |YT, Yt - 1, . . . . ).
Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?
Consider the time series xt = β1 + β2t + wt, where β1 and β2 are known constants and wt is a white noise process with variance σ2 w. (a) Determine whether xt is stationary. (b) Show that the process yt = xt − xt−1 is stationary. (c) Show that the mean of the moving average vt = 1 2q + 1 q j=−q xt−j is β1 + β2t, and give a simplified expression for the autocovariance function.
2. Suppose that Yt follows the stationary AR (1) model Yt=2.5+0.7Yt−1+ϵt, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=9. a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations of Yt d) Suppose that YT=102.3. Compute Yt+1|t=E(Yt+1|Yt,Yt-1...)
2. Suppose that Yt follows the stationary AR (1) model Yt=2.5+0.7Yt−1+ϵt, where ϵt is i.i.d. with E(ϵt)=0 and Var(ϵt)=9. a) Compute the mean and variance of Yt b) Compute the first two autocovariances of Yt c) Compute the first two autocorrelations of Yt d) Suppose that YT=102.3. Compute Yt+1|t=E(Yt+1|Yt, Yt-1...). Kindly note, sub-parts (a), (b) & (c) are solved alread.
Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0
Assess whether the following AR (1) process satisfies the criteria for covariance stationarity, taking into consideration all three conditions that define a covariance stationary process. Assume that u~i.i.d(0, var_u), where var_u = 1. Provide the working steps and underlying assumptions used to prove if each property holds. y_t = 2 + 0.3y_(t-1)+u_t
Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2

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1. Suppose that Y, follows the Moving Average process of order 1 (MA(1)) model Y₁ = Et - 0&t-1, where &t is i.i.d. with E(E+) = 0 and Var(t) = 0². a) Compute the mean and variance of Y b) Compute the first two autocovariances of Y c) Compute the first two autocorrelations of Y