1. Suppose that Y, follows the Moving Average process of order 1 (MA(1)) model Y = E – 0ɛ;-1: where &t is i.i.d. with E(ɛ) = 0 andVar(s) = o?.a) Compute the mean and variance of Yb) Compute the first two autocovariances of Y,c) Compute the first two autocorrelations ofY,

Given Yt follows the moving average process of order 1 . Yt=εt-θεt-1 where εtis independent and…

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

See similar textbooks

Similar questions

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
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, . . . . ).
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
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, .... 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?
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.
The joint probability mass function p(x,y) of X and Y is defined as follows: p(0,0)=0.5 p(1,0)=0.2 p(0,1)=0.2 p(1,1)=0.1 a) What is the covariance between X and Y? b) What is the correlation coefficient of X and Y? c) Are X and Y are dependent? What about are X and Y are uncorrelated?
Let X and Y have the following joint distribution:X \Y 0 1 0 0.40 0.10 1 0.10 0.10 2 0.10 0.20 d.) Calculate the covariance between X and Y e.) Find σ2x and σ2y
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
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.

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

1. Suppose that Y, follows the Moving Average process of order 1 (MA(1)) model Y₁ = Et -0t-1, where &t is i.i.d. with E(&t) = 0 and Var(t) = o². a) Compute the mean and variance of Y b) Compute the first two autocovariances of Y c) Compute the first two autocorrelations of Y