Restricted Structural Change Models

Methods for detecting structural breaks and estimating break locations for linear multiple regression models under general linear restrictions on the coefficient vector. Restrictions can be within regimes, across regimes, or both, and are supported in two forms: an affine parameterization (Form A: delta = S*theta + s) and explicit linear constraints (Form B: R*delta = r). Provides break date estimation with confidence intervals, a restricted sup-F test for the null of no structural change, simulation of critical values by Monte Carlo, and a bootstrap restart procedure to reduce the risk of convergence to spurious local optima. Also implements a generalized regression tree (linear model tree) procedure where each leaf contains a linear regression model rather than a local average. Reference: Perron, P., and Qu, Z. (2006). 'Estimating Restricted Structural Change Models.' Journal of Econometrics, 134(2), 373-399. .

rbreak

Restricted Structural Change Models

Overview

Methods for detecting structural breaks and estimating break locations under linear restrictions on coefficients within and across regimes using the method of Perron and Qu (2006).

Example

library(rbreak)

# Example data
data(example)
y <- example$y
bigt <- length(y)
z <- matrix(1, nrow = bigt, ncol = 1)

# Form A restrictions: coefficients in regimes 1 and 3 are equal, coefficients in regimes 2 and 4 are equal
m <- 3
q <- 1
trm <- 0.10
S <- matrix(c(1, 0,
              0, 1,
              1, 0,
              0, 1), nrow = 4, byrow = TRUE)
s <- rep(0, 4)

# Complete analysis
result_formA <- mainp(
  m = m, q = q, z = z, y = y, trm = trm,
  robust = 0, prewhit = 0, hetvar = 1,
  S = S, s = s,
  doestim = 1, dotest = 0, docv = 0,
  bigt = bigt, forma = 1, formb = 0
)

# Form B restrictions: coefficients in regimes 1 and 3 are equal, coefficients in regimes 2 and 4 are equal
R <- matrix(c(1, 0, -1, 0,
              0, 1,  0, -1), nrow = 2, byrow = TRUE)
r <- c(0, 0)

# Complete analysis
result_formB <- mainp(
  m = m, q = q, z = z, y = y, trm = trm,
  robust = 0, prewhit = 0, hetvar = 1,
  R = R, r = r,
  doestim = 1, dotest = 0, docv = 0,
  bigt = bigt, forma = 0, formb = 1
)

References

Perron, P., and Qu, Z. (2006). "Estimating Restricted Structural Change Models". Journal of Econometrics, 134(2), 373-399. doi:10.1016/j.jeconom.2005.06.030

Bai, J., and Perron, P. (1998). "Estimating and Testing Linear Models with Multiple Structural Changes". Econometrica, 66(1), 47-78.

Bai, J., and Perron, P. (2003). "Computation and Analysis of Multiple Structural Change Models". Journal of Applied Econometrics, 18(1), 1-22.