Hansen B. (2001), The New Econometrics of Structural Change:
Dating Breaks in U.S. Labor Productivity,
Journal of Economic Perspectives, 15, 117–128.
Zeileis A., Leisch F., Kleiber C., Hornik K. (2005), Monitoring
Structural Change in Dynamic Econometric Models,
Journal of Applied Econometrics, 20, 99–121.
Examples
data("durab")
## use AR(1) model as in Hansen (2001) and Zeileis et al. (2005)
durab.model <- y ~ lag
## historical tests
## OLS-based CUSUM process
ols <- efp(durab.model, data = durab, type = "OLS-CUSUM")
plot(ols)
## F statistics
fs <- Fstats(durab.model, data = durab, from = 0.1)
plot(fs)
## F statistics based on heteroskadisticy-consistent covariance matrix
fsHC <- Fstats(durab.model, data = durab, from = 0.1,
vcov = function(x, ...) vcovHC(x, type = "HC", ...))
plot(fsHC)
## monitoring
Durab <- window(durab, start=1964, end = c(1979, 12))
ols.efp <- efp(durab.model, type = "OLS-CUSUM", data = Durab)
newborder <- function(k) 1.723 * k/192
ols.mefp <- mefp(ols.efp, period=2)
ols.mefp2 <- mefp(ols.efp, border=newborder)
Durab <- window(durab, start=1964)
ols.mon <- monitor(ols.mefp)
ols.mon2 <- monitor(ols.mefp2)
plot(ols.mon)
lines(boundary(ols.mon2), col = 2)
## Note: critical value for linear boundary taken from Table III
## in Zeileis et al. 2005: (1.568 + 1.896)/2 = 1.732 is a linear
## interpolation between the values for T = 2 and T = 3 at
## alpha = 0.05. A typo switched 1.732 to 1.723.
## dating
bp <- breakpoints(durab.model, data = durab)
summary(bp)
plot(summary(bp))
plot(ols)
lines(breakpoints(bp, breaks = 1), col = 3)
lines(breakpoints(bp, breaks = 2), col = 4)
plot(fs)
lines(breakpoints(bp, breaks = 1), col = 3)
lines(breakpoints(bp, breaks = 2), col = 4)