"Frontmatter". In: Analysis of Financial Time Series

REGRESSION MODELS WITH TIME SERIES ERRORS 69(a) Change in 1-year rateper. chg.-2 -1 0 1 21970 1980 1990 2000year(b) Change in 3-year rateper. chg.-2 -1 0 1 21970 1980 1990 2000yearFigure 2.15. Time plots of the change series of U.S. weekly interest rates from January 12,1962 to September 10, 1999: (a) changes in the Treasury 1-year constant maturity rate, and(b) changes in the Treasury 3-year constant maturity rate.The unit-root behavior of both interest rates and the residuals of Eq. (2.40) leadsto the consideration of the change series of interest rates. Let1. c 1t = r 1t − r 1,t−1 = (1 − B)r 1t for t ≥ 2: Changes in the 1-year interest rate;2. c 3t = r 3t − r 3,t−1 = (1 − B)r 3t for t ≥ 2: Changes in the 3-year interest rate,and consider the linear regression c 3t = α+βc 1t +e t . Figure 2.15 shows time plots ofthe two change series, whereas Figure 2.13(b) provides a scatterplot between them.The change series remain highly correlated with a fitted linear regression modelgiven byc 3t = 0.0002 + 0.7811c 1t + e t , ˆσ e = 0.0682, (2.41)with R 2 = 84.8%. The standard errors of the two coefficients are 0.0015 and 0.0075,respectively. This model further confirms the strong linear dependence betweeninterest rates. Figure 2.16 shows the time plot and sample ACF of the residuals ofEq. (2.41). Once again, the ACF shows some significant serial correlation in theresiduals, but the magnitude of the correlation is much smaller. This weak serial