FIN 5309 Homework 7 – Fall 2021
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
FIN 5309 Homework 7 – Fall 2021
Instructions
a. You can either write down your assignment or type it in a word file or a combination of both. Please submit it in Moodle and make sure it is clear to see if you scan your handwritten homework.
b. Unless explicitly stated otherwise, solve every question manually. Your answers will be graded both on your demonstrated understanding of the concepts from the book and from the class, as well as the clarity of your explanations.
c. For any R application, including the screenshots of both commands and results in your homework will allow us to more easily give partial credit.
d. No late submissions will be accepted, except with prior permission.
Instruction for Problem 1 and 2.
• All tests use the 5% significance level for type-I error.
• For daily series, use ten (10) lags in all ACF or ARCH-effect tests. For monthly series, use twelve (12) lags.
• The purpose of these R application is to analyze the volatility series of daily and monthly asset returns. All models include both the mean and volatility equations. You should always perform model checking to confirm the adequacy of a fitted model.
1. [40 points] R application
Consider the daily returns of Amazon (amzn) stock from January 2, 2009 to December 31, 2014. The simple returns are available from CRSP and in the file d-amzn3dx0914.txt (the column with heading amzn) on Moodle. Transform the simple returns to log returns. Multiple the log returns by 100 to obtain the percentage returns. Let be the percentage log returns.
setwd(" … ")
require(fGarch)
da<-read.table("d-amzn3dx0914.txt",header=T)
head(da)
rt=log(da$amzn+1)*100
(a) Is the expected value of zero? Why? Are there any serial correlations in ? Why? (b) Fit a Gaussian ARMA-GARCH model to the series. Obtain the normal QQplot of the standardized residuals, and write down the fitted model. Is the model adequate? Why? (c) Build an ARMA-GARCH model with Student-t innovations for the log return series. Perform model checking and write down the fitted model.
(d) Obtain 1-step to 5-step ahead mean and volatility forecasts using the fitted ARMA- GARCH model with Student-t innovations.
2. [60 points] R application
Consider the daily log returns of Caterpillar stock (CAT) from January 3, 2006 to April 15, 2017. You may download the data using quantmod. Let be the log returns, which can be obtained via
require(quantmod)
getSymbols("CAT",from="2006-01-03",to="2017-04- 15")
head(CAT)
rtn <- diff(log(as.numeric(CAT[,6])))
(a) Are there any serial correlations in the log return series ? Why?
(b) Are there any ARCH effects in the log return series ? Why?
(c) Fit a Gaussian ARMA-GARCH model to the series. Perform model checking, including showing the normal QQ-plot ofthe standardized residuals. Is the model adequate? Write down the fitted model.
(d) Build a GARCH model with standardized Student-t innovations for the series. Perform model checking, including the QQ-plot. Is the model adequate? Why? (e) Write down the fitted model.
(f) Obtain 1-step to 5-step ahead mean and volatility forecasts using the fitted ARMA- GARCH model with standardized Student-t innovations.
2021-12-11