Homework Help is Here – Start Your Trial Now!
Math
Statistics
Q5. GLS and MLE Consider the model where yt = x₁p+ut, t= 1,..., T utput-1+€t, t=...,0,1,2,..., with |p|<1, and {e) is a sequence of i.i.d. disturbances, with E(e)=0, Var(e) = o², vt. a) Explain how the above linear regression could be transformed to make the disturbances i.i.d. (when p is un- known). b) Discuss how p and ß could be estimated in the above model by Generalized Least Square (GLS) method. c) Discuss how you could estimate the above model by Maximum Likelihood Estimation (MLE) method, i.e. write down the log-likelihood function, replace the parameter o2 in the likelihood and derive the first order condi- tions. d) Do you need any additional assumptions in order to apply MLE?

Q5. GLS and MLE Consider the model where yt = x₁p+ut, t= 1,..., T utput-1+€t, t=...,0,1,2,..., with |p|<1, and {e) is a sequence of i.i.d. disturbances, with E(e)=0, Var(e) = o², vt. a) Explain how the above linear regression could be transformed to make the disturbances i.i.d. (when p is un- known). b) Discuss how p and ß could be estimated in the above model by Generalized Least Square (GLS) method. c) Discuss how you could estimate the above model by Maximum Likelihood Estimation (MLE) method, i.e. write down the log-likelihood function, replace the parameter o2 in the likelihood and derive the first order condi- tions. d) Do you need any additional assumptions in order to apply MLE?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Q5. GLS and MLE Consider the model Yt = x;B+ut, t=1,..., T where Uf = put-1+€t, t=.,0, 1,2,..., with |p| < 1, and {e}, is a sequence of i.i.d. disturbances, with t=1 E(€;) = 0, Var(e;) = o²,vt. a) Explain how the above linear regression could be transformed to make the disturbances i.i.d. (when p is un- known). b) Discuss how p and 6 could be estimated in the above model by Generalized Least Square (GLS) method. c) Discuss how you could estimate the above model by Maximum Likelihood Estimation (MLE) method, i.e. write down the log-likelihood function, replace the parameter o? in the likelihood and derive the first order condi- tions. d) Do you need any additional assumptions in order to apply MLE ?
Transcribed Image Text:Q5. GLS and MLE Consider the model Yt = x;B+ut, t=1,..., T where Uf = put-1+€t, t=.,0, 1,2,..., with |p| < 1, and {e}, is a sequence of i.i.d. disturbances, with t=1 E(€;) = 0, Var(e;) = o²,vt. a) Explain how the above linear regression could be transformed to make the disturbances i.i.d. (when p is un- known). b) Discuss how p and 6 could be estimated in the above model by Generalized Least Square (GLS) method. c) Discuss how you could estimate the above model by Maximum Likelihood Estimation (MLE) method, i.e. write down the log-likelihood function, replace the parameter o? in the likelihood and derive the first order condi- tions. d) Do you need any additional assumptions in order to apply MLE ?
Expert Solution
steps

Step by step

Solved in 6 steps with 64 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS