psiii245b

# psiii245b - (c Suppose that you had to estimate f X ϖ How...

This preview shows page 1. Sign up to view the full content.

University of California D. Steigerwald Department of Economics Economics 245B Problem Set III 1. Consider a sequence of observations on a random variable X t , where t=1,...,T. (a) Suppose you are given the power spectral density function for X, f X ( ϖ ), for ϖ ε [0, π ]. What can you say about {X t } from an examination of f X ( ϖ )? What does it mean for X t to be nonstationary and how can you use f X ( ϖ ) to detect this? How does this method relate to detecting nonstationarity using the time domain approach? (b) Carefully explain the concept of aliasing. Describe how the Nyquist (or folding) frequency is determined.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (c) Suppose that you had to estimate f X ( ϖ ). How would you construct your estimator? What problems would arise if X t is nonstationary? 2. Give the definition of a periodic function and its period. For the trigonometric function A sin ϖ x carefully define: its period, angular frequency, amplitude, and phase. 3. Write down a Fourier series representation of the function f(x) which has period p. Please describe the influence of each of the first four terms and intuitively explain why your representation defines a function with period p....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern