Note: For Problem #1, write your answers into a Jupyter Notebook …le and submit the …
(2) Using Python, perform the following for the KOSPI index returns during the period 2021:01:02-2021:12:30 (on the basis of daily, closing prices; data available at https://ecos.bok.or.kr/‡ex/EasySearch.jsp).
Plot the sample autocorrelation function of the simple returns of the KOSPI index (log-di¤erences of the index). Do they indicate serial corre-lation?
Test the null of no serial correlation using the Ljung-Box test at the 5% level. Set the lag length at 10.
(3) 1Suppose that the daily log return of a security follows the model
rt = 0:01 + 0:2rt 1 + at
where fatg is a Gaussian white noise series with mean zero and variance 0.02.
What are the mean and variance of the return series rt?
Compute the lag-1 and lag-2 autocorrelations of rt .
Assume that r100 = 0:01, and r99 = 0:02. Compute the 1- and 2-step ahead forecasts of the return series at the forecast origin T = 100. What are the associated standard deviations of the forecast errors?
(1) Suppose that rt is represented by the AR(2) process
rt = 1:1rt 1 0:4rt 2 + at; at W N(0; 2):
Is this process stationary?
4. (1) Consider the process
X1
rt = 1 + 0:2j at j ; at W N(0; 2):
j=0
Is this process stationary?
2
5. (1) Find the ACF function of the MA(2) process
rt = at + 1at 1 + 2at 2; at W N(0; 2):
