Homework Help is Here – Start Your Trial Now!
Math
Statistics
A time series with a periodic component can be constructed from xt = U1 sin(2πω0t) + U2 cos(2πω0t), where U1 and U2 are independent random variables with zero means and E(U2 1 ) = E(U2 2 ) = σ2. The constant ω0 determines the period or time it takes the process to make one complete cycle. Show that this series is weakly stationary with autocovariance function

A time series with a periodic component can be constructed from xt = U1 sin(2πω0t) + U2 cos(2πω0t), where U1 and U2 are independent random variables with zero means and E(U2 1 ) = E(U2 2 ) = σ2. The constant ω0 determines the period or time it takes the process to make one complete cycle. Show that this series is weakly stationary with autocovariance function

MATLAB: An Introduction with Applications
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
icon
Related questions
Question

A time series with a periodic component can be constructed from
xt = U1 sin(2πω0t) + U2 cos(2πω0t),
where U1 and U2 are independent random variables with zero means and
E(U2
1 ) = E(U2
2 ) = σ2. The constant ω0 determines the period or time it
takes the process to make one complete cycle. Show that this series is weakly
stationary with autocovariance function
γ(h) = σ2 cos(2πω0h

1.9 A time series with a periodic component can be constructed from Xt = U1 sin(2Twot) + U2 cos(2Twot), where U1 and U2 are independent random variables with zero means and E(U?) = E(U;) takes the process to make one complete cycle. Show that this series is weakly stationary with autocovariance function o2. The constant wo determines the period or time it y(h) = o² cos(2™woh).
Transcribed Image Text:1.9 A time series with a periodic component can be constructed from Xt = U1 sin(2Twot) + U2 cos(2Twot), where U1 and U2 are independent random variables with zero means and E(U?) = E(U;) takes the process to make one complete cycle. Show that this series is weakly stationary with autocovariance function o2. The constant wo determines the period or time it y(h) = o² cos(2™woh).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
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