Macroeconometrics作业代写 Stata代写

Macroeconometrics 6: ARMA Applications and Introduction to VARs (Graded HW Problems)

Macroeconometrics作业代写 Repeat part (a) but now for the growth rate of u, which you should create and name d1ogu (i.e., the first difference of 1ogu).

Note: Please solve problems 3 through 5 im a simgle Stata .do file called HW6CONTÆOL.

1.Consider the following ARMA(1,2) process:

If you know that the process is invertible, then what conditions must the parametersø1, θ₁, and θ2 satisfy when the process is set up in its pure MA representation?

2.Consider the following ARMA(2,1) process:

If you know that the process is invertible, then what conditions do you know the parameters ø1, ø2, and ø3 must satisfy when the process is set up in its pure AR representation?

3.The dataset HW6.dta contains: Macroeconometrics作业代写

ap1 (the average product of labor in the US) u (the levelof unemployment in the US) 1f (the level of the labor force in the US) v (the level of vacancies in the US) and quarcer (a time variable).

(a)Usethe ac command to generate an autocorelation graph for the natural logarithm of u, which you should create and call 1ogu¡ call this graph ac1ogu and use the rep1ace and nodrau commands. Do the same using the pac command and naming the graph pac1ogu. Then, use the graph combine command to generate a combined graph with pac1ogu on the left-hand side and ac1ogu on the right-hand side. Call this last graph combineu1. Write down in your Stata code as comments your conclusions about Explain your reasoning. Macroeconometrics作业代写

(b)Repeat part (a) but now for the growth rate of u, which you should create and name d1ogu (i.e., the first difference of 1ogu). Call the autocorrelations graph acd1ogu, the partial autocorrelations graph pacd1ogu, and the combined graph combineu2. (Write down in your Stata code as comments your conclusions about Explain your reasoning.)

(c)Repeat part (a) but now for the cyclical component of the natural logarithm of u, which you should create and name C1ogu using an HP filter with smoothing parameter equal to fi600. Call the autocorrelations graph acC1ogu, the partial autocorrelations graph pacC1ogu, and the combined graph combineu3. (Write down in your Stata code as comments your conclusions about Explain your reasoning.)

(d)Repeat part (c) but now using an HP filter with smoothing parameter equal to 10⁵.

Call the cyclical component C21ogu. Call the autocorrelations graph acC21ogu,the partial autocorrelations graph pacC21ogu, and the combined graph combineu4. (Write down in your Stata code as comments your conclusions about Explain your reasoning.)

(e)Considermodeling 1ogu, d1ogu, C1ogu, and C21ogu as ARMA processes using the Box Jenkins What would be your choice of starting order for each of these processes given your results in (a), (b), (c), and (d)? Write down in your Stata code your conclusions as comments and explain your reasoning.

(f)Model(i.e., write Stata code for) d1ogu and C1ogu as ARMA For each of these variable use all the steps of the Box Jenkins approach, and control for ARCH and GARCH, modifying the specifications as needed for heteroskedasticity. Write down in your Stata code as comments your justification for each step that you take. Finally, given your preferred bottom-line specification for each process, decide which you would prefer to use. Please explain your reasoning as comments in your Stata code.

4.Model (i.e., write Stata code for) d1ogu and C1ogu using Stata‘s suite of VAR com- mands. Macroeconometrics作业代写

The steps are: selecting an optimal lag order, checking for stability, Write downusing comments in your Stata code a justification for each of the steps that you take. You will now have 4 specifications for these variables: 2 from problem 3, and 2 from this problem. Which of these would be your preferred specification? Please explain your reasoning as comments in your Stata code.

5.Generate impulse response functions to a fi-unit shock for 30 periods for each of the 4 specifications you‘ve arrived at as of problem 3, included, and plot each of these impulse responses in a single graph (i.e., 4 graphs total, all in a single graph). Also, generate one-step-ahead predictions for each of the 4 specifications you‘re arrived at and plot each of these predictions along with the empirical data series that each of these corresponds to in a single graph (i.e., 4 graphs total, all in a single graph). Macroeconometrics作业代写

Write down in your Stata code as comments a description of what you observe in each of the impulse response function graphs and elaborate on the extent to which they differ. Do the same for the graphs pertaining to the one-step-ahead predictions. Also, please comment on the following: do the IRF and one-step-ahead predictions change in any way your conclusions about a preferred specification relative to problem (4)?

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