Consider the AR (2) model: Yt9-1 + 2Y1-2 + 1 = where f-1~ N(0, 72) and...

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Consider the AR (2) model: Yt9-1 + 2Y1-2 + 1 = where f-1~ N(0, 72) and f-1 is all available information up to and including time t- 1. We have a sample from this model: y = (yr). Set yo=y-1 = 0. Tasks: Show all working out in your answers 1. (2 marks) Derive the conditional likelihood function: Le(, 7|y) = P(U, 92, 9r|V, 7). The conditioning here is on yoy-1 = 0. 2. (2 marks) Find an expression for the negative of the logarithm of the conditional likelihood in Task 1, i.e. - log Le(, 7|y). 3. (4 marks) Differentiate the negative of the log-likelihood in Task 2, with respect to each unknown parameter, then write down the set of equations that need to be solved to find the mles. 4. (3 marks) Solve the equations in Task 3 to find formulas for the mles for this model Consider the AR (2) model: Yt9-1 + 2Y1-2 + 1 = where f-1~ N(0, 72) and f-1 is all available information up to and including time t- 1. We have a sample from this model: y = (yr). Set yo=y-1 = 0. Tasks: Show all working out in your answers 1. (2 marks) Derive the conditional likelihood function: Le(, 7|y) = P(U, 92, 9r|V, 7). The conditioning here is on yoy-1 = 0. 2. (2 marks) Find an expression for the negative of the logarithm of the conditional likelihood in Task 1, i.e. - log Le(, 7|y). 3. (4 marks) Differentiate the negative of the log-likelihood in Task 2, with respect to each unknown parameter, then write down the set of equations that need to be solved to find the mles. 4. (3 marks) Solve the equations in Task 3 to find formulas for the mles for this model

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To derive the necessary likelihood function negative loglikelihood and equations for finding the Max... View the full answer