FIN 5309 Homework 6 – Spring 2021
Due May 17, 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.
1. (30 points) Consider the following autocorrelation and partial autocorrelation coefficients estimated using 500 observations for a weakly stationary series, yt:
Lag | acf | pacf
1 | 0.307 | 0.307
2 | -0.013 | 0.264
3 | 0.086 | 0.147
4 | 0.031 | 0.086
5 | -0.197 | 0.049
a. Using a simple ‘rule of thumb’, determine which, if any, of the acf and pacf coefficients are significant at the 5% level.
b. Use both the Box-Pierce and the Ljung–Box statistics to test the joint null hypothesis that the first five autocorrelation coefficients are jointly zero.
c. What process would you tentatively suggest that could represent the most appropriate model for the series? Explain your answer.
2. (10 points) You obtain the following estimates for an ARMA model of some returns data
rt = 0.6rt-1 + ut - 1.3ut-1 + 0.4ut-2
where ut is a white noise error process. By examining the characteristic equation, check the estimated model for stationarity.