rq.break: Testing for Breaks and Estimating Break Dates and Sizes with...

In QR.break: Structural Breaks in Quantile Regression

Testing for Breaks and Estimating Break Dates and Sizes with Confidence Intervals

Description

This is the main function of this package for testing breaks in quantile regression models and estimating break dates and break sizes with corresponding confidence intervals.

Usage

rq.break(y, x, vec.tau, N, trim.e, vec.time, m.max, v.a, v.b, verbose)

Arguments

y	a numeric vector, the outcome variable (NT x 1), the first N units are from the first period, the next N from the second period, and so forth.
x	A matrix of regressors (NT x p), structured in the same way as y, a column of ones will be automatically added to x.
vec.tau	a numeric vector, quantiles used for break estimation, for example vec.tau = seq(0.20, 0.80, by = 0.10)
N	a numeric vector, the number of cross-sectional units. Set to 1 for a time series quantile regression.
trim.e	a scalar between 0 and 1, the trimming proportion. For example, if trim.e=0.1, the minimum regime length is 0.1 times the data span.
vec.time	a vector of dates, needed for reporting the estimated break dates, in the format of (starting date...ending date); If set to NULL, the break dates will be reported as indices (e.g., 55 for the 55th observation in the sample).
m.max	the maximum number of breaks allowed.
v.a	the significance level used for determining the number of breaks; 1, 2 or 3 for 10%, 5% or 1%, respectively
v.b	the coverage level for constructing the confidence intervals of break dates; 1 or 2 for 90% and 95%, respectively.
verbose	Logical; set to TRUE to print estimates to the console. Default is FALSE.

Value

A list containing:

• ⁠$s.out⁠: A list with break testing results, estimated break dates, confidence intervals, and coefficient estimates based on individual quantiles.

• ⁠$m.out⁠: A list with break testing results, estimated break dates, confidence intervals, and coefficient estimates obtained by testing and estimating breaks using multiple quantiles simultaneously.

Each list (s.out or m.out) contains:

• test_tau: A matrix of test statistics and critical values for break detection at quantile tau.

• nbreak_tau: The number of detected breaks at quantile tau.

• br_est_tau: A matrix of estimated break dates and their confidence intervals at quantile tau.

• br_est_time_tau: The same as br_est_tau, but with break dates reported in calendar format (if vec.time is provided and is not NULL).

• coef_tau: Estimated regression coefficients for each regime at quantile tau.

• bsize_tau: Break size estimates for each transition between regimes at quantile tau.

References

Koenker, R. and G. Bassett Jr. (1978). Regression quantiles. Econometrica, 46(1), 33-50.

Oka, T. and Z. Qu (2011). Estimating Structural Changes in Regression Quantiles. Journal of Econometrics, 162(2), 248-267.

Qu, Z. (2008). Testing for Structural Change in Regression Quantiles. Journal of Econometrics, 146(1), 170-184.

Examples

## Example 1
## Time series example, using GDP data
## data
data(gdp)
y        = gdp$gdp
x        = gdp[,c("lag1", "lag2")]
vec.time = gdp$yq

## the maximum number of breaks allowed
m.max = 3

## the signifance level for sequenatial testing
## 1, 2 or 3 for 10%, 5% or 1%, respectively
v.a = 2

## the significance level for the confidence intervals of estimated break dates.
## 1 or 2 for 90% and 95%, respectively.
v.b = 2

## the size of the cross-section
N = 1

## the trimming proportion for estimating the break dates
## (represents the minimum length of a regime; used to exclude
## the boundaries of the sample)
trim.e = 0.15

## quantiles
vec.tau = seq(0.20, 0.80, by = 0.150)

verbose = FALSE #do not print

## main estimation
res = rq.break(y, x, vec.tau, N, trim.e, vec.time, m.max, v.a, v.b, verbose)

QR.break documentation built on June 8, 2025, 1:53 p.m.