ECO 521 Quantitative Methods II Spring Semester 2020
Problem Set 3
These problems are due by Friday, April 24, 2020, at midnight. No exceptions! You should submit a copy of the SAS program you wrote in order to solve the problem, the SAS output, and of course your analysis of and solution to the problem. You will have to e-mail me the solutions and you will probably have to supply a separate document that explains your work. I cannot print all your problem sets, so they will have to be in a form that I can read electronically.
Important note: Because these problem sets are a part of your course grade, you should treat them as a kind of take-home test. Thus, maintaining academic intergrity is impor- tant. The work you turn in should be yours and yours alone in every aspect. If you are stuck and in need of assistance, you should be contacting me.
late problem sets will not be accepted!
1. Suppose {et : t = −1, 0, 1, . . .} is a sequence of iid random variables with mean zero and variance 1. Define a stochastic process by
xt =et −0.5et−1 +0.5et−2,t=1,2, … a. Is xt stationary? Show your work.
b. Is xt weakly dependent? Again, show your work.
2. Determine whether each of the following series has a unit root or not. If applicable, also determine whether each series has drift or trend. Use both the methods of Enders and Elder & Kennedy. I also want you to assess whether the series is growing or not growing, based on a visual inspection of the series. In other words, you should do this first.
The series to analyze are:
a. The U.S. industrial production index, starting from January 1980 (FRED mnemonic: INDPRO);
b. The U.S. trade balance in goods and services, balance of payments basis, starting from January 1992 (FRED mnemonic: BOPGSTB), and
c. Thetotalbusinessinventoriestosalesratio,startingfromJanuary1992(FREDmnemonic: ISRATIO).
You will need to go to the St. Louis Fed’s FRED website to download the series. In case you need them, the critical values from Enders are:
• To test the null that trend = 0 given a unit root: 2.79 (for α = 0.05) and 3.53 (for α = 0.01);
• To test the null that drift = 0 given a unit root: 2.54 (for α = 0.05) and 3.22 (for α = 0.01.)