Perform some nonlinearity tests and draw the conclusion

Question

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_1t and r_3t, respectively, and the data span is from January 5, 1962 to September 10, 1999. The data are in files w-gs3yr.txt and w-gs1yr.txt on the Web and can be obtained from the Federal Reserve Bank of St. Louis.

(a) Let s_t = r_3t - r_1t be the spread in log interest rates. Is {s_t} linear? Perform some nonlinearity tests and draw the conclusion using the 5% significance level.

(c) Build a threshold model for the s_t series and check the fitted model.

(d) Build a threshold model for the  series and check the fitted model.