Problem 1

Consider the Nile data once more:

data(Nile)
Nile <- window( Nile, 1900, 1970 ) T <- length(Nile)
y <- Nile/1000

Program the conditional and exact log-likelihood functions of an MA(1) model and fnd ML estimates using the optim routine.

Problem 2

The fle infation.csd contains quarterly data on U.S. infation from 160n:Q1 to 2n17:Q4.

(a) Model the series with an appropriate ARMA model.

(b) You want to calculate 1-step-ahead forecasts for the period 168n:Q1 to 2n17:Q4. You use moding window forecasts with a window width of 0n quarters/data points. Thus, you use data from 1605:Q1 to 1676:Q4 to forecast infation in 168n:Q1, data from 1605:Q2 to 168n:Q2 to forecast infation in 168n:Q2, and so on.

Calculate forecasts using i) a random walk, ii) an AR(1) model, iii) an AR(2) model and id) an AR(4) model.
(c) Plot the true dalues of infation and all 4 forecast series in one graph.

(d) Calculate the MSFE and the MAFE for the 4 forecast series. Which model forecasts best?

(e) Use the Diebold-Mariano test in order to check whether the diferences in (d) are signifcant.

Problem 3

Get daily return data for an asset of your choice and ft the series with an appropriate GARCH model.

Note:

Explain every stage and process, so there is no word limit but clear explanations.

Priority should be given to question number 3

Please hand in the work as follows

Question 1
1) R code used in readable format on a word document without any commentary
2) R code as a machine-readable file that can be opened on any R program in Workfile format
3) solution on a word document showing again r code and any commentary or explanation on how things were done

Question 2

1) R code used in readable format on a word document without any commentary
2) R code as a machine-readable file that can be opened on any R program in Workfile format
3) solution on a word document showing again r code and any commentary or explanation on how things were done

Question 3

Please take daily stock price of the company Biogen for the last 5 years

1) R code used in readable format on a word document without any commentary
2) R code as a machine-readable file that can be opened on any R program in Workfile format
3) solution on a word document showing again r code and any commentary or explanation on how things were done
4) All diagrams should be clearly printed and sent over
5) an excel file saved in csv of the Biogen daily stock price for last 5 years used for the task.