Take Home Midterm Exam

Time-Series Econometrics

Fall Semester, 2011.

Please note that use a word process when you turn in your answer sheet. Otherwise, I will not read!

Due date: 11/14(Monday)/2011

1. The first column in file sim.xls contains the 100 values of the simulated ARMA(p,q) process. Use this series and perform the following tasks.

a) Plot the sequence against time. Does this series appear to be stationary? Explain.

b) Plot and tabulate the first 24 coefficients of the sample ACF and the sample PACF. Based on your ACF and PACF, suggest a candidate ARMA(p,q) process that you believe as the true process for this simulated series. You should specify your reasons for your suggestion. Tip: you don’t need to include a constant term in your ARMA process.

c) Together your suggested ARMA(p,q) process, also consider an ARMA(1,1) process without a constant term as an alternative possible process. Then, estimate the parameters of the two ARMA(p,q) process (i.e. your ARMA(p,q) and ARMA(1,1)) and decide which one is the best process to describe the simulated series. You could use t-statistic, AIC and BIC etc.

d) Finally, based on Ljung-Box Q statistics of the ARMA(1,1) and your ARMA(p,q) process, verify that your final decision is correct.

2. The second column in file sim.xls also contains the 100 values of the simulated ARMA(p,q) process.

a) Plot and tabulate the first 12 coefficients of the sample ACF and the sample PACF.

b) Based on your ACF and PACF, suggest an ARMA(p,q) process that you believe as the true process for this simulated series. You also should specify your reasons for your suggestion. Tip: you don’t need to include a constant term in your ARMA process.

c) Together your suggested ARMA(p,q) process, also consider a MA(2) process without a constant term as an alternative possible process. Then, estimate the parameters of the two ARMA(p,q) processes (i.e. your ARMA(p,q) and MA(2)) and decide which one is the best process. You could use t-statistic, AIC and BIC etc.

d) Finally, based on Ljung-Box Q statistics of the MA(2) and your ARMA(p,q) process, verify that your final decision is correct.

e) Explain “what is parsimonious model” in Box-Jenkins modeling philosophy.