ECON 323代写、代做R设计、R语言编程代做

日期：2020-10-20 10:53

Assignment #4 – ECON 323 – Fall 2020

Professor Mikal Skuterud

Date assigned: October 6, 2020 at 7:00

Date due: October 19, 2020 at 23:30

1. Consider the time-series process {????????} defined by the data generating process ???????? = ???? +

???????? for all ???? = 1, … , where {????????} is an i.i.d. normally distributed sequence with mean zero

and variance ????????

2 = 4. The random variable ???? does not change over time (so it is

uncorrelated with ????????) and comes from a discrete uniform distribution in the closed

interval [0;100].

a. Produce 20 realizations of this time-series process with ???? = 100. Graph all 20

realizations in a graph similar to those produced in the section 2(2) slides.

Interpret your graph. Does it appear that the process is stationary? Does it

appear to be weakly dependent? Justify your answer.

b. Analytically (i.e., using a pen and paper instead of R) find the expected value and

variance of ????????. Do your answers depend on ????? Interpret.

c. Find ????????????(????????, ????????+?) for any ???? and ?. Is ???????? covariance stationary? Justify your

answer?

d. Find ????????????????(????????, ????????+?). Does ???????? appear to be weakly dependent? Justify your

answer.

2. Consider the time-series process ???????? defined by the data generating process ???????? = cos(????????)

for all ???? = 1, … , where ???? is a random variable with a continuous uniform distribution in the

open interval (0; 2????) and cos(?) is the cosine function.

a. Produce 10 realizations of this time-series process with ???? = 50. Graph all 10

realizations in a graph. Interpret your graph. Does it appear that the process is

covariance stationary? Does it appear to be weakly dependent? Justify your

answer.

b. Using R or your pen and paper or any other resource, find the expected value,

variance, and covariances of ???????? to determine whether the process is covariance

stationary. Justify your answer.

c. Is the process strongly (sometimes called “strictly”) stationary? Why or why not?

Justify your answer.