Answered: Find the mean xt , E(Xt) and the…

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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Economics

Now suppose that the time series process {X_t}, is expressed as X_t = z + e_twhere e_t is iid with a mean of zero and a variance of σ , and the variable z does not change over time (time invariant) which means it has a mean E(z) = 0 and , and it is assumed that z and e_t are uncorrelated:

i. Find the mean x_t , E_(Xt)and the variance X_t, var(X_t). Do they depend on t?

ii. Determine the covariance of x_t and x_t+h for h > 0, Cov(X_t, x_t+h)

iii. Is x_t stationary? Explain.

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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