Because of the existence of inverted yield curves in the term structure of interest rates, the spread of interest rates should be nonlinear. To verify this, consider the weekly U.S. interest rates of (a) Treasury 1-year constant maturity rate, and (b) Treasury 3-year constant maturity rate. As in Chapter 2, denote the two interest rates by \(r_{1 t}\) and \(r_{3 t}\), respectively, and the data span is from January 5, 1962 to September 10, 1999. The data are in files "wgs3yr.dat" and "wgs1yr.dat" on the Web.
- Let \(s_{t}=r_{3 t}-r_{1 t}\) be the spread in log interest rates. Is \(\left\{s_{t}\right\}\) linear? Perform some nonlinearity tests and draw the conclusion using the \(5 \%\) significance level.
- Let \(s_{t}^{*}=\left(r_{3 t}-r_{3, t-1}\right)-\left(r_{1 t}-r_{1, t-1}\right)=s_{t}-s_{t-1}\) be the change in interest rate spread. Is \(\left\{s_{t}^{*}\right\}\) linear? Perform some nonlinearity tests and draw the conclusion using the \(5 \%\) significance level.
- Build a threshold model for the \(s_{t}\) series and check the fitted model.
- Build a threshold model for the \(s_{t}^{*}\) series and check the fitted model.