Consider the model where y = x + u, t= 1,.., T U =put-1+E, t=...,0,1,2,..., with...

   

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Consider the model where y₁ = x₁ + u, t= 1,.., T U₁ =put-1+E, t=...,0,1,2,..., with lpl<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 f.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? Consider the model where y₁ = x₁ + u, t= 1,.., T U₁ =put-1+E, t=...,0,1,2,..., with lpl<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 f.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?

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a To transform the above linear regression model to make the disturbances 11d we can use the CochraneOrcutt method The steps involved are as follows 1 ... View the full answer