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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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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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 ?
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