The Federal Reserve Bank of St Louis publishes selected interest rates and U.S. financial data on its Web site:

\[ \text { http://www.stls.frb.org/fred/index.html } \]

Consider the monthly 1-year and 10 -year Treasury constant maturity rates from April 1953 to October 2000 for 571 observations; see the file "m-gs1n10.dat." The rates are in percentages.

(a) Let \(c_{t}=r_{t}-r_{t-1}\) be the change series of the monthly interest rate \(r_{t}\). Build a bivariate autoregressive model for the two change series. Discuss the implications of the model. Transform the model into a structural form.

(b) Build a bivariate moving-average model for the two change series. Discuss the implications of the model and compare it with the bivariate AR model built earlier.

(c) Are the two monthly interest rate series co-integrated?