Package 'sysbreak' reference manual

Title:	Structural Breaks in a System of Equations
Description:	Methods for detecting, estimating, and conducting inference on multiple structural breaks in a linear system of equations, such as multivariate linear regressions, seemingly unrelated regressions, vector autoregressions, and network vector autoregressions. Breaks can occur in the regression coefficients, the covariance matrix of the errors, or both, and can be restricted to a subset of the coefficients. The main function, sysbreak(), returns the number of breaks detected and confidence intervals for the break dates and for the regression coefficients. A separate function ordbreak() estimates ordered breaks, in which a break in one subset of equations occurs before a break in another. Specialized functions for vector autoregressions varbreak() and network vector autoregressions netbreak() are also provided. Reference: Qu, Z., and Perron, P. (2007). 'Estimating and Testing Structural Changes in Multivariate Regressions.' Econometrica, 75(2), 459-502.
Authors:	Zhongjun Qu [aut, cre], Cheolju Kim [aut], Pierre Perron [aut]
Maintainer:	Zhongjun Qu <[email protected]>
License:	GPL (>= 3)
Version:	1.1.0
Built:	2026-10-31 18:58:55 UTC
Source:	https://github.com/cran/sysbreak

Methods to Examine What Changes at Each Break Date

Description

For each estimated break date, tests whether the volatilities, the correlations and the regression coefficients differ between the two regimes on either side of it.

Usage

brtype(fit)
brtype(fit)

Arguments

fit

A result from sysbreak, varbreak or netbreak with at least one break.

Details

The volatility statistic is a two-sample Hotelling (1931) statistic on the squared residuals. The correlation statistic is the Jennrich (1970) test for equal correlation matrices, which assumes normal errors. The coefficient statistic is a Wald test for equal coefficients; it covers only the coefficients allowed to change, and is NA when no coefficient is allowed to change. Each test compares the two regimes adjacent to a break and treats the break dates as known.

The coefficient test holds the error covariance constant across regimes, even when fit allows it to break (brv = TRUE). Estimating the covariance separately in each regime would make the test oversized in samples of typical length; the constant covariance tends to make it conservative when the volatility does change.

Value

A data frame with one row per break: breaks, the break date as a row of the data; the statistics volatility, correlation and coefficients; and their p-values volatility_p, correlation_p and coefficients_p. The degrees of freedom are $n$ , $n(n-1)/2$ and the number of coefficients allowed to change.

References

Hotelling, H. (1931). The generalization of Student's ratio. The Annals of Mathematical Statistics, 2(3), 360-378.

Jennrich, R. I. (1970). An asymptotic chi-square test for the equality of two correlation matrices. Journal of the American Statistical Association, 65, 904-912.

Examples

set.seed(11)
bigt <- 120
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[61:120] <- y1[61:120] + 1.2 - 0.6 * x[61:120]
dat <- data.frame(y1 = y1, y2 = y2, x = x)

fit <- sysbreak(cbind(y1, y2) ~ x, data = dat, m = 2, trim = 0.2)
brtype(fit)

set.seed(11)
bigt <- 120
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[61:120] <- y1[61:120] + 1.2 - 0.6 * x[61:120]
dat <- data.frame(y1 = y1, y2 = y2, x = x)

fit <- sysbreak(cbind(y1, y2) ~ x, data = dat, m = 2, trim = 0.2)
brtype(fit)

GAUSS/MATLAB Example Data 1

Description

Example data used by the original GAUSS/MATLAB mbreak2 script. In this package the corresponding procedure is sysbreak.

Usage

data1
data1

Format

A numeric matrix with 150 rows and 5 columns. Columns 1 and 2 are dependent variables, and columns 3 through 5 are regressors.

Source

Qu, Z., and Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica, 75(2), 459-502.

GAUSS/MATLAB Example Data 2

Description

Example data used by the original GAUSS/MATLAB obreak2 script for the ordered-break procedure.

Usage

data2
data2

Format

A numeric matrix with 100 rows and 5 columns. Columns 1 and 2 are dependent variables, and columns 3 through 5 are regressors.

Source

Qu, Z., and Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica, 75(2), 459-502.

Diebold-Yilmaz Spillover Measures Without Breaks

Description

Fits a VAR by OLS on the whole sample and computes the generalized spillover measures of dyspill(), for comparison with the measures of a model with breaks.

Usage

dynobreak(y, lags, h, intercept = TRUE)
dynobreak(y, lags, h, intercept = TRUE)

Arguments

y

Numeric matrix, one column per variable.

lags

Positive integer number of lags.

h

Positive integer forecast horizon.

intercept

Logical; include an intercept.

Value

A list with the row-normalized generalized fevd, the total spillover index total, and the directional vectors from, to and net. The covariance divides by the number of observations.

Examples

set.seed(1)
bigt <- 120
a <- matrix(c(0.2, 0.4, 0.4, 0.2), 2)
y <- matrix(0, bigt, 2)
colnames(y) <- c("y1", "y2")
for (tt in 2:bigt) {
  y[tt, ] <- a %*% y[tt - 1, ] + rnorm(2, sd = 0.3)
}

sp <- dynobreak(y, lags = 1, h = 10)
sp$total
sp$net

set.seed(1)
bigt <- 120
a <- matrix(c(0.2, 0.4, 0.4, 0.2), 2)
y <- matrix(0, bigt, 2)
colnames(y) <- c("y1", "y2")
for (tt in 2:bigt) {
  y[tt, ] <- a %*% y[tt - 1, ] + rnorm(2, sd = 0.3)
}

sp <- dynobreak(y, lags = 1, h = 10)
sp$total
sp$net

Diebold-Yilmaz Generalized Spillover Measures

Description

Computes horizon-specific spillover measures from a fitted structural-break VAR model. The forecast-error variance decomposition uses generalized shocks and is therefore invariant to variable ordering.

Usage

dyspill(fit, h = 10, boot = 0, seed = NULL)
dyspill(fit, h = 10, boot = 0, seed = NULL)

Arguments

fit

A fitted object returned by varbreak() or netbreak().

h

Positive integer for forecast horizon.

boot

Number of bootstrap replications for standard errors and confidence intervals; 0 for none. Available for varbreak() and netbreak() fits.

seed

Optional seed for the bootstrapping. The seed of the calling session is restored on exit.

Details

For a regime-specific VAR,

$y_t = c_r + \sum_{\ell=1}^p A_{\ell,r}y_{t-\ell}+u_t,\qquad E(u_tu_t')=\Sigma_r,$

let $\Psi_{0,r}=I$ and

$\Psi_{s,r}=\sum_{\ell=1}^{\min(p,s)} A_{\ell,r}\Psi_{s-\ell,r}.$

The generalized variance share from shock $j$ to variable $i$ is

$\theta_{ij}^{g}(H)= \frac{\sigma_{jj}^{-1}\sum_{s=0}^{H-1} (e_i'\Psi_s\Sigma e_j)^2} {\sum_{s=0}^{H-1}e_i'\Psi_s\Sigma\Psi_s'e_i}.$

Rows are normalized to sum to one before spillover statistics are formed. For variable $i$ , from is the contribution received from all other shocks, to is the contribution transmitted to all other variables, and net = to - from; a positive net value identifies a net transmitter. The total spillover index is the average off-diagonal contribution, expressed in percent.

The benchmark puts every lag matrix to zero and keeps $\Sigma_r$ . The measures then depend on the error correlations only; comparing them with the fitted ones shows how much of the spillover comes from the dynamics. With two variables the benchmark total is $100\rho^2/(1+\rho^2)$ .

The bootstrap is a recursive residual bootstrap within each regime: the residuals of the regime are resampled, the series is rebuilt from the fitted VAR of the regime, the model is refitted at the same break dates in the same way as fit, and the measures are recomputed. The break dates are treated as known. The intervals are percentile intervals, since the draws are skewed in small samples. Draws in which a refitted VAR is not stable are dropped.

Value

An object of class "dyspill" containing:

horizon

The forecast horizon h.

model

The source model type.

variables

Names of the endogenous variables.

break_grid

A data frame with one row per regime: the regime number; its first and last observation, start and end, counted in the estimation sample (which omits the first lags observations); and the coefficient and covariance regimes it belongs to, coef_regime and cov_regime.

regimes

A list with one entry per regime. Each entry contains:

input_rows: the first and last row of the data in the regime.
spectral_radius: the largest modulus of the eigenvalues of the companion matrix of the VAR; the VAR is stable when it is below one.
fevd: the generalized forecast-error variance decomposition, with rows normalized to sum to one.
total: the total spillover index.
from, to and net: the directional spillovers of each variable.
net_pairwise: the matrix of net pairwise spillovers.
benchmark_total and benchmark_net: total and net recomputed with all lag coefficients set to zero, so that they reflect the error correlations only (see Details).
With boot > 0: the bootstrap standard errors total_se and net_se, and the percentile intervals total_ci and net_ci.

boot

Returned only when boot > 0. A list with:

replications: the number of bootstrap replications.
level: the coverage probability of the intervals, taken from ci_level of the fit.
total: the bootstrap draws of the total index, a matrix with one row per replication and one column per regime.
net: the bootstrap draws of the net spillovers, an array of replications by variables by regimes.
differences: a data frame with one row per pair of regimes, giving the difference in the total index (the later regime minus the earlier one), its bootstrap standard error se, and the percentile interval lower and upper.
dropped: the number of draws dropped in each regime because the refitted VAR was not stable.

References

Diebold, F. X., and Yilmaz, K. (2012). Better to give than to receive: Predictive directional measurement of volatility spillovers. International Journal of Forecasting, 28(1), 57–66.

Examples

set.seed(1)
bigt <- 120
y <- matrix(0, bigt, 2)
colnames(y) <- c("y1", "y2")
for (tt in 2:bigt) {
  a <- if (tt > 60) matrix(c(0.2, 0.6, 0.6, 0.2), 2) else diag(0.2, 2)
  y[tt, ] <- a %*% y[tt - 1, ] + rnorm(2, sd = 0.3)
}

fit <- varbreak(y, lags = 1, m = 1, trim = 0.2)
dyspill(fit, h = 10, boot = 99, seed = 1)

set.seed(1)
bigt <- 120
y <- matrix(0, bigt, 2)
colnames(y) <- c("y1", "y2")
for (tt in 2:bigt) {
  a <- if (tt > 60) matrix(c(0.2, 0.6, 0.6, 0.2), 2) else diag(0.2, 2)
  y[tt, ] <- a %*% y[tt - 1, ] + rnorm(2, sd = 0.3)
}

fit <- varbreak(y, lags = 1, m = 1, trim = 0.2)
dyspill(fit, h = 10, boot = 99, seed = 1)

U.S. House Prices and the Macroeconomy

Description

Quarterly data for the house price application of Ahamada and Diaz Sanchez (2013), 1959:Q4 to 2009:Q3.

Usage

housing
housing

Format

A data frame with 200 rows and 6 columns:

date: Quarter, such as "1960:Q1".
dGDP: Log difference of real GDP.
dC: Log difference of real personal consumption expenditures.
dHP: Log difference of the real home price index.
FFR: Federal funds rate, in percent, first month of the quarter.
dI: Change in FFR.

Source

FRED series GDPC1, PCEC, CPIAUCSL and FEDFUNDS, and the Shiller nominal home price index, seasonally adjusted by log-STL. Consumption and home prices are deflated by CPIAUCSL.

References

Ahamada, I., and Diaz Sanchez, J. L. (2013). A retrospective analysis of the house price macro-relationship in the United States. International Journal of Central Banking, 9(4), 153-174.

International Inflation

Description

Monthly consumer price inflation for the G7 countries and the euro area, 1973:04 to 2007:12, from Bataa, Osborn, Sensier and van Dijk (2013).

Usage

inflation
inflation

Format

A data frame with 417 rows and 9 columns: date, such as "1973:04", followed by inflation for Canada, EuroArea, France, Germany, Italy, Japan, UK and US. Inflation is $100 \times \Delta \log$ of the consumer price index, adjusted for outliers and seasonality by the authors.

Source

The replication files of Bataa et al. (2013).

References

Bataa, E., Osborn, D. R., Sensier, M., and van Dijk, D. (2013). Structural breaks in the international dynamics of inflation. Review of Economics and Statistics, 95(2), 646-659.

Structural Breaks in a network VAR

Description

Estimates structural breaks in a VAR whose coefficients are restricted by a fixed network matrix. With one lag, the model is

$y_t = \mu_j + (\alpha_{1,j} W + \beta_{1,j} I)y_{t-1} + u_t,$

for observations in regime $j$ . With multiple lags, the model is

$y_t = \mu_j + \sum_{\ell=1}^p (\alpha_{\ell,j} W + \beta_{\ell,j} I)y_{t-\ell} + u_t.$

Usage

netbreak(y, W, lags, m, intercept = TRUE,
  coef_breaks = "all", row_normalize = FALSE,
  test_level = 0.05, ci_level = 0.95,
  trim = 0.15, verbose = FALSE, brv = FALSE,
  robust = c("none", "hc", "hac"), hetq = FALSE, prewhit = FALSE,
  restart = c("none", "brbp", "brbp_residual"),
  restart_B = 10, restart_verbose = FALSE, h = NULL)
netbreak(y, W, lags, m, intercept = TRUE,
  coef_breaks = "all", row_normalize = FALSE,
  test_level = 0.05, ci_level = 0.95,
  trim = 0.15, verbose = FALSE, brv = FALSE,
  robust = c("none", "hc", "hac"), hetq = FALSE, prewhit = FALSE,
  restart = c("none", "brbp", "brbp_residual"),
  restart_B = 10, restart_verbose = FALSE, h = NULL)

Arguments

y

Numeric matrix/data frame with one column per network node.

W

Numeric square network matrix. Row $i$ gives the weights used to form the network lag for equation $i$ .

lags

Positive integer, number of lags.

m

The maximum number of breaks allowed.

intercept

Logical. If TRUE, include equation-specific intercepts $\mu_i$ .

coef_breaks

Parameters allowed to change across regimes. The parameters are one intercept per node, mu:<node>; the network coefficients $\alpha_\ell$ , named network_lag1, network_lag2, and so on; and the own-lag coefficients $\beta_\ell$ , named own_lag1, own_lag2, and so on. The default "all" lets every parameter change. "none" or NULL holds them all constant, which requires brv = TRUE so that the disturbance covariance matrix can change; otherwise the code will return an error message. For anything in between, supply a character vector of parameter names or of these groups:

"intercepts", or "mu": all $\mu_i$ .
"network": all $\alpha_\ell$ .
"own": all $\beta_\ell$ .
"dynamic": every lag coefficient, network and own.
"lag1", "lag2", ...: $\alpha_\ell$ and $\beta_\ell$ at that lag.
"alpha1", "beta1", ...: $\alpha_\ell$ or $\beta_\ell$ on its own.

Entries are case-insensitive and may be combined, as in c("intercepts", "network_lag1").

row_normalize

Logical. If TRUE, row-normalize W; rows with zero row sums are left as zero rows.

test_level

Significance level used for selecting the number of breaks. One of 0.10, 0.05, 0.025 or 0.01. WDmax decides whether there is any break; if it is not significant the procedure stops and no break is reported. Otherwise the sequential tests of $l$ against $l+1$ breaks are applied from one break upwards, stopping at the first insignificant test or at m.

ci_level

Coverage probability of the reported confidence intervals for the break dates. Either 0.95 or 0.90.

trim

Trimming parameter. The minimum segment length is h = round(trim * nrow(y)). We recommend $h \ge 3(n + k)$ , where $n$ is the number of equations and $k$ the number of regressors per equation, and a larger value for larger systems. A warning is issued if $h < 3(n + k)$ .

verbose

Logical. If TRUE, print additional progress information from the testing and estimation.

brv

Logical. If TRUE, allow the disturbance covariance matrix to change across regimes.

robust

Inference for the coefficient-break tests, the coefficient standard errors and the break-date confidence intervals. "none" gives Gaussian quasi-likelihood-ratio tests, valid when the errors are serially uncorrelated and conditionally homoskedastic. "hc" gives the robust SupF statistic of Qu and Perron (2007, eq. 20) with a heteroskedasticity-consistent covariance estimate without autocovariance terms, valid when the errors are a martingale difference sequence. "hac" uses instead the quadratic spectral kernel with the automatic bandwidth of Andrews (1991), allowing for serial correlation. With enough lags the VAR errors are serially uncorrelated, and "hc" suffices for the tests and standard errors; with brv = TRUE and conditionally heteroskedastic errors of the ARCH type, the confidence intervals require "hac".

hetq

Logical. If TRUE, allow regressor moments to vary across regimes when computing confidence intervals for break dates.

prewhit

Logical. If TRUE, prewhiten the scores by a VAR(1) before the HAC estimation (Andrews and Monahan, 1992). Used only when robust = "hac".

restart

A bootstrap restarting procedure to check and improve convergence. It applies only when some coefficients are held constant; otherwise it is ignored with a warning. Set to "none" to turn it off, "brbp" for resampling bootstrap restarts, or "brbp_residual" for residual-based restarts.

restart_B

Integer, number of restart values used when restart != "none".

restart_verbose

Logical. If TRUE, print restart progress.

h

Optional positive integer for forecast horizon. If supplied, attach Diebold–Yilmaz generalized spillover measures in spillover.

Details

The interpretation of testing$statistic depends on robust.

robust = "none" gives the SupLR statistic. The code can test the parameters specified by coef_breaks, the disturbance covariance when brv = TRUE, or both.
robust = "hc" or "hac" gives the robust SupF statistic, for the parameters only, because the covariance-break critical values are case dependent under heteroskedasticity or serial correlation; it assumes a constant error covariance. With brv = TRUE, the estimates, standard errors and confidence intervals account for the covariance breaks; under "hc" the intervals further require errors without ARCH-type dependence.

Value

An object of class c("netbreak", "sysbreak") containing:

spec: A summary of the setup, including the sample size bigt, the number of equations n, the total number of NVAR parameters per regime q, the arguments m, lags, intercept, row_normalize, trim, brv, robust, hetq, prewhit, test_level and ci_level, the network matrix W, the equation and parameter names, the retained input rows y_rows after discarding the lags, and a record of the coef_breaks selector.
testing: The tests, reported at test_level: statistic, testing no break against $k$ breaks for every $k = 1,\ldots,m$ , with its critical_values; statistic_type, "SupLR" or "SupF", and NA when a requested robust test is unavailable; wdmax and wdmax_critical_values; the sequential tests of $l$ against $l+1$ breaks, each containing l, a statistic and its critical_values; and the number of changing_parameters, which includes the changing covariance parameters when robust = "none".
br_selected: The outcome of the break-number determination at test_level: the selected number of breaks, the WDmax statistic with its critical value and significance flag, and the sequential steps taken. breaks is 0 when WDmax is not significant, and NA when the tests are unavailable for the requested specification.
estimation: The estimates related to the selected number of breaks: estimated breaks; their confidence intervals ci_breaks; coefficients by regimes and their confidence intervals; disturbance covariance matrices. This component is NULL when no break is detected, in which case only testing and br_selected are informative.
spillover: When h is supplied and at least one break is selected, regime-specific Diebold–Yilmaz generalized spillover measures returned by dyspill.
y: The responses used in estimation, rows spec$y_rows of y.

Note that m is the maximum number of breaks allowed. Testing output is reported for every value from 1 through m, while estimation corresponds to the number of breaks selected by the procedure under test_level. Parameters excluded by coef_breaks are repeated across regime blocks. The optional spillover component is omitted when h = NULL. The fit has print(), summary(), plot() and the accessors in sysbreak-methods.

References

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59(3), 817–858.

Andrews, D. W. K., and Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60(4), 953–966.

Zhu, X., Pan, R., Li, G., Liu, Y., and Wang, H. (2017). Network vector autoregression. The Annals of Statistics, 45(3), 1096–1123.

Qu, Z., and Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica, 75(2), 459–502.

Examples

set.seed(5)
bigt <- 80
W <- matrix(c(0, 1, 1, 0), 2, 2, byrow = TRUE)
y <- matrix(0, bigt, 2)
colnames(y) <- c("y1", "y2")
for (tt in 2:bigt) {
  alpha <- if (tt <= 40) 0.05 else 0.75
  beta <- 0.1
  y[tt, ] <- alpha * as.numeric(W %*% y[tt - 1, ]) +
    beta * y[tt - 1, ] + rnorm(2, sd = 0.2)
}

fit <- netbreak(
  y = y, W = W, lags = 1, m = 1,
  coef_breaks = c("network", "own"),
  trim = 0.2
)
fit$estimation$breaks

set.seed(5)
bigt <- 80
W <- matrix(c(0, 1, 1, 0), 2, 2, byrow = TRUE)
y <- matrix(0, bigt, 2)
colnames(y) <- c("y1", "y2")
for (tt in 2:bigt) {
  alpha <- if (tt <= 40) 0.05 else 0.75
  beta <- 0.1
  y[tt, ] <- alpha * as.numeric(W %*% y[tt - 1, ]) +
    beta * y[tt - 1, ] + rnorm(2, sd = 0.2)
}

fit <- netbreak(
  y = y, W = W, lags = 1, m = 1,
  coef_breaks = c("network", "own"),
  trim = 0.2
)
fit$estimation$breaks

Simulated Network VAR

Description

One draw from Scenario 1 of Han and Lee (2024): a network VAR for 20 nodes over 300 periods, with breaks after periods 100 and 200.

Usage

netsim
netsim

Format

A list with two components:

y: A 300 by 20 matrix of observations, with columns node1 to node20.
W: The 20 by 20 row-normalized network matrix. Entry $(i, l)$ is $1/n_i$ if node $i$ follows node $l$ and 0 otherwise, where $n_i$ is the number of nodes that $i$ follows.

Details

In regime $j$ ,

$y_{it} = V_i'\gamma_j + \sum_{\ell} \alpha_{\ell,j} (W y_{t-\ell})_i + \sum_{\ell} \beta_{\ell,j} y_{i,t-\ell} + e_{it}, \qquad e_{it} \sim N(0, 0.1^2).$

Regime 1 has one lag, with $\alpha = -0.10$ and $\beta = 0.20$ . Regimes 2 and 3 have two lags, with $\alpha = (0.20, -0.22)$ , $\beta = (-0.12, 0.40)$ and $\alpha = (-0.12, 0.10)$ , $\beta = (0.25, -0.40)$ . The covariates $V_i$ are fixed, so $V_i'\gamma_j$ is a node intercept that changes across regimes. The in-degrees of the network follow a power law, as in Zhu et al. (2017).

Source

Simulated with set.seed(1) following Han and Lee (2024).

References

Han, Y., and Lee, T. C. M. (2024). Structural break detection in non-stationary network vector autoregression models. IEEE Transactions on Network Science and Engineering, 11(5), 4134-4145.

Zhu, X., Pan, R., Li, G., Liu, Y., and Wang, H. (2017). Network vector autoregression. The Annals of Statistics, 45(3), 1096-1123.

Ordered Structural Breaks in a System of Equations

Description

Estimation of a multiple-equation system in which the coefficients of one group of equations change before those of another group. The two break dates are estimated jointly and are not restricted to coincide.

Usage

ordbreak(set1, set2, data,
  coef_breaks1 = "all", coef_breaks2 = "all",
  trim = 0.2, hetq = TRUE, max_break_gap = NULL,
  test_level = 0.05, ci_level = 0.95,
  confidence_intervals = FALSE,
  ci_grid_radius = 20, ci_replications = 5000, ci_step = 1000,
  ci_grid_step = 0.02, ci_seed = NULL, ci_verbose = FALSE,
  tol = 1e-8, max_iter = 1000)
ordbreak(set1, set2, data,
  coef_breaks1 = "all", coef_breaks2 = "all",
  trim = 0.2, hetq = TRUE, max_break_gap = NULL,
  test_level = 0.05, ci_level = 0.95,
  confidence_intervals = FALSE,
  ci_grid_radius = 20, ci_replications = 5000, ci_step = 1000,
  ci_grid_step = 0.02, ci_seed = NULL, ci_verbose = FALSE,
  tol = 1e-8, max_iter = 1000)

Arguments

set1

The equations whose coefficients change at the first date. A formula such as y1 ~ x1 + x2 for a single equation, or list(y1 ~ x1 + x2, y2 ~ x2 + x3) for several. The number of regressors may differ across equations. An intercept is added to each equation unless the formula indicates otherwise.

set2

The equations whose coefficients change at the second date, written in the same way as set1. Each equation of the system belongs to exactly one of the two sets.

data

Data frame used to evaluate the formulas.

coef_breaks1

An expression for which coefficients of set1 are allowed to change at the first date. The default "all" allows all of them to change. Otherwise supply a list of formulas, one per equation of set1, where the left-hand side should specify the equation and the right-hand side selects the coefficients of that equation that may change:

y1 ~ x1: the intercept and the coefficient on x1 change.
y1 ~ x1 - 1: the coefficient on x1 only.
y1 ~ 0: no coefficient of that equation changes.

Coefficients left out are held constant across both dates. At least one coefficient of set1 must be allowed to change.

coef_breaks2

The same, for set2 and the second date.

trim

Trimming parameter, which must lie in $(0, 0.5)$ . The minimum segment length is floor(trim * nrow(data)).

hetq

Logical. If TRUE, allow regressor moments to vary across regimes when computing confidence intervals for break dates.

max_break_gap

Truncation used when computing the test statistic. If NULL, floor(sqrt(T)) is used, as in the original GAUSS program.

test_level

Significance level at which the critical value is reported. One of 0.10, 0.05, 0.025 or 0.01.

ci_level

Coverage probability of the reported confidence intervals for the break dates. Either 0.95 or 0.90.

confidence_intervals

Logical. If TRUE, simulate confidence intervals for the two break dates. This is the expensive part of the procedure and is therefore off by default.

ci_grid_radius

Half-width of the grid on which the limiting distribution is simulated.

ci_replications

Number of simulation replications.

ci_step

Number of steps used to discretize each Brownian motion.

ci_grid_step

Spacing of the simulation grid.

ci_seed

Optional seed for the simulation. The seed of the calling session is restored on exit.

ci_verbose

Logical. If TRUE, print simulation progress.

tol

Convergence tolerance of the feasible GLS iterations.

max_iter

Maximum number of feasible GLS iterations.

Details

The coefficients are stacked equation by equation in the order the formulas are given, so those of set1 occupy the leading q1 positions and those of set2 the remaining q2. ordcheck reports this layout without estimating anything, which is worth doing before a long run.

The test is that of Qu and Perron (2007, Section 6.4) for locally ordered breaks. The test for globally ordered breaks in their Section 6.5, whose limiting distribution differs, is not implemented.

Value

An object of class "ordbreak" containing:

spec: The setup: the sample size bigt, the number of equations n, the minimum segment length h, the number of coefficients in each set q1 and q2, the number of equations in the first set n1, the names of the coefficients allowed to change at each date, changing1 and changing2, the arguments trim, hetq and trun, the input formulas split into set1 and set2, the equation and coefficient names, the retained data rows y_rows after discarding missing values, and the selection matrix S.
testing: The SupLR statistic for ordered breaks, sup_lr_ordered, its critical_values at test_level, the pair truncated_breaks the statistic is computed at, and the log-likelihoods H1like and H0like it is built from. The critical value is indexed by the number of coefficients allowed to change, not by the total number of coefficients.
estimation: The estimated breaks, given as rows of data; the coefficients beta1 and beta2 of the two regimes; the residuals of the model at the estimated breaks, one column per equation; and the coefficient shifts delta1 and delta2 occurring at the two dates; and ci_breaks, a two by two matrix when confidence_intervals = TRUE and NULL otherwise, also given as rows of data. Its rows are the two break dates and its columns the lower and upper bounds at ci_level.

Note that the ordering is imposed rather than tested. The equations in set1 are taken to break first, so exchanging the two sets specifies a different model. Both specifications are tested against the same no-break null, and their values of sup_lr_ordered can be compared.

References

Qu, Z., and Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica, 75(2), 459–502.

Examples

set.seed(13)
bigt <- 60
x1 <- rnorm(bigt)
x2 <- rnorm(bigt)
y1 <- 1 + 0.5 * x1 + rnorm(bigt, sd = 0.3)
y2 <- 1 + 0.5 * x2 + rnorm(bigt, sd = 0.3)
y1[21:bigt] <- y1[21:bigt] + 1.5 * x1[21:bigt]
y2[36:bigt] <- y2[36:bigt] - 1.5 * x2[36:bigt]
dat <- data.frame(y1 = y1, y2 = y2, x1 = x1, x2 = x2)

fit <- ordbreak(y1 ~ x1, y2 ~ x2, data = dat, trim = 0.2)
fit$estimation$breaks

set.seed(13)
bigt <- 60
x1 <- rnorm(bigt)
x2 <- rnorm(bigt)
y1 <- 1 + 0.5 * x1 + rnorm(bigt, sd = 0.3)
y2 <- 1 + 0.5 * x2 + rnorm(bigt, sd = 0.3)
y1[21:bigt] <- y1[21:bigt] + 1.5 * x1[21:bigt]
y2[36:bigt] <- y2[36:bigt] - 1.5 * x2[36:bigt]
dat <- data.frame(y1 = y1, y2 = y2, x1 = x1, x2 = x2)

fit <- ordbreak(y1 ~ x1, y2 ~ x2, data = dat, trim = 0.2)
fit$estimation$breaks

Coefficient Layout of an Ordered-Break Specification

Description

Reports the coefficients of an ordered-break model, which set of equations they belongs to, and which of them are allowed to change, without estimating anything.

Usage

ordcheck(set1, set2, data, coef_breaks1 = "all", coef_breaks2 = "all")
ordcheck(set1, set2, data, coef_breaks1 = "all", coef_breaks2 = "all")

Arguments

set1

The equations whose coefficients change at the first date, written as in ordbreak.

set2

The equations whose coefficients change at the second date.

data

Data frame used to evaluate the formulas.

coef_breaks1

Which coefficients of set1 are allowed to change at the first date. See ordbreak.

coef_breaks2

The same, for set2 and the second date.

Value

The layout is printed: one row per coefficient, giving its position in the coefficient vector, its name, the set it belongs to, whether it is allowed to change, and the date at which it changes.

Examples

set.seed(13)
dat <- data.frame(y1 = rnorm(40), y2 = rnorm(40),
                  x1 = rnorm(40), x2 = rnorm(40))

ordcheck(y1 ~ x1 + x2, y2 ~ x1 + x2, data = dat,
        coef_breaks1 = list(y1 ~ x1))

set.seed(13)
dat <- data.frame(y1 = rnorm(40), y2 = rnorm(40),
                  x1 = rnorm(40), x2 = rnorm(40))

ordcheck(y1 ~ x1 + x2, y2 ~ x1 + x2, data = dat,
        coef_breaks1 = list(y1 ~ x1))

Plot a Structural-Break Fit

Description

Plots each series with the estimated break dates (dashed lines), their confidence intervals (shaded) and, optionally, the fitted values of the regime-specific model.

Usage

## S3 method for class 'sysbreak'
plot(x, which = NULL, dates = NULL, fitted = TRUE, ...)
## S3 method for class 'sysbreak'
plot(x, which = NULL, dates = NULL, fitted = TRUE, ...)

Arguments

x

A fit returned by sysbreak, varbreak or netbreak.

which

Series to plot, as indices or names. By default all series, or the first four when there are more.

dates

Optional vector with one entry per row of the data passed to the fitting function, including the initial lags of a VAR and any rows dropped for missing values; the observation in row r is placed at dates[r]. Numeric values or dates are used as the horizontal axis; character values, such as "1983:Q1", are used as labels for the axis.

fitted

Logical. If TRUE, add the fitted values.

...

Graphical parameters. type, col, lwd, lty and pch apply to the plotted series; main and ylab may be vectors with one entry per panel; the others, such as xlab, ylim or las, are passed to plot() when each panel is set up.

Value

x, invisibly.

Examples

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)
fit <- sysbreak(cbind(y1, y2) ~ x, dat, m = 1, trim = 0.3)
plot(fit)

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)
fit <- sysbreak(cbind(y1, y2) ~ x, dat, m = 1, trim = 0.3)
plot(fit)

Summarize a Structural-Break Fit

Description

A report of a fit returned by sysbreak, varbreak or netbreak: the break number, the break dates with their confidence intervals, and a coefficient table for each regime. print() of the fit gives the full output.

Usage

## S3 method for class 'sysbreak'
summary(object, ...)

## S3 method for class 'summary.sysbreak'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'sysbreak'
summary(object, ...)

## S3 method for class 'summary.sysbreak'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

object

A fit returned by sysbreak(), varbreak() or netbreak().

...

Not used.

x

An object returned by summary().

digits

Number of significant digits in the coefficient tables.

Value

An object of class "summary.sysbreak", a list with the model type, the numbers of equations n and observations bigt, the tests for the break-number decision, the number of breaks selected, and, when at least one break is selected, the break dates with their confidence intervals (breaks), the rows of the data in each regime (regimes) and the coefficient tables (coefficients): estimate, standard error, $z$ value and two-sided $p$ -value, one table per regime, treating the break dates as known.

Examples

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)
fit <- sysbreak(cbind(y1, y2) ~ x, dat, m = 1, trim = 0.3)
summary(fit)

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)
fit <- sysbreak(cbind(y1, y2) ~ x, dat, m = 1, trim = 0.3)
summary(fit)

Structural Breaks in a System of Equations

Description

Estimation of a multiple-equation system affected by structural breaks in the regression coefficients and/or the variance covariance matrix of the residuals.

Usage

sysbreak(model, data = NULL, m, coef_breaks = "all",
  test_level = 0.05, ci_level = 0.95,
  trim = 0.15, verbose = FALSE, brv = FALSE,
  robust = c("none", "hc", "hac"), hetq = FALSE, prewhit = FALSE,
  restart = c("none", "brbp", "brbp_residual"),
  restart_B = 10, restart_verbose = FALSE)
sysbreak(model, data = NULL, m, coef_breaks = "all",
  test_level = 0.05, ci_level = 0.95,
  trim = 0.15, verbose = FALSE, brv = FALSE,
  robust = c("none", "hc", "hac"), hetq = FALSE, prewhit = FALSE,
  restart = c("none", "brbp", "brbp_residual"),
  restart_B = 10, restart_verbose = FALSE)

Arguments

model

A formula such as cbind(y1, y2) ~ x1 + x2 for a system with common regressors across equations, or list(y1 ~ x1 + x2, y2 ~ x2 + x3) for a system allowing different regressors across equations. The number of regressors may differ across equations, e.g., list(y1 ~ x1 + x2, y2 ~ x3) An intercept is added to each equation unless the formula indicates otherwise.

data

Data frame used to evaluate model.

m

Integer, the maximum number of breaks allowed when testing for breaks.

coef_breaks

An expression for which regression coefficients are allowed to change across regimes. The default "all" allows all regression coefficients to change. "none" or NULL restrictions all coefficients to be constant. \ This case requires setting brv = TRUE, so that the disturbance covariance matrix\ can change; otherwise the code will return an error message. For in between, supply a list of formulas, one per equation, where left-hand side should specify the equation and the right-hand side selects the coefficients of that equation that may change:

y1 ~ x1, y2 ~ x2: the coefficient on x1 in the first equation and the coefficient on x2 in the second equation can change.
y1 ~ 1, y2 ~ x2+ x4: the intercept in the first equation and the two slope coefficients in the second equation.
y1 ~ 1 + x1, y2~0: the intercept and x1 in the first equation, and no coefficient in the second equation.

test_level

Significance level used to select the number of breaks. One of 0.10, 0.05, 0.025 or 0.01. The double-maximum tests decide whether there is any break; if WDmax is not significant the procedure stops and no break is reported. Otherwise the sequential tests of $l$ against $l+1$ breaks are applied from one break upwards, stopping at the first insignificant test or at m.

ci_level

Coverage probability of the reported confidence intervals for the break dates. Either 0.95 or 0.90.

trim

verbose

Logical. If TRUE, print additional information from the estimation.

brv

Logical. If TRUE, allow the covariance matrix of the residuals to change across regimes.

robust

hetq

Logical. If TRUE, allow regressor moments to vary across regimes when computing confidence intervals for break dates.

prewhit

Logical. If TRUE, prewhiten the scores by a VAR(1) before the HAC estimation (Andrews and Monahan, 1992). Used only when robust = "hac".

restart

restart_B

Number of restarting values used when restart != "none"; 10 is recommended.

restart_verbose

Logical. If TRUE, print restart progress.

Details

The interpretation of testing$statistic depends on robust.

robust = "none" gives the SupLR statistic. The code can test the coefficients specified by coef_breaks, the disturbance covariance when brv = TRUE, or both.
robust = "hc" or "hac" gives the robust SupF statistic, for the coefficients only, because the covariance-break critical values are case dependent under heteroskedasticity or serial correlation; it assumes a constant error covariance. With brv = TRUE, the estimates, standard errors and confidence intervals account for the covariance breaks; under "hc" the intervals further require errors without ARCH-type dependence.

Value

An object of class "sysbreak" containing:

spec: A summary of the setup, including the sample size bigt, the number of equations n, the total number of regression coefficients per regime q, the arguments m, trim, brv, robust, hetq, prewhit, test_level and ci_level, the input formula or formulas, the equation and coefficient names, the retained data rows y_rows after discarding missing values, and a record of the coef_breaks selector.
testing: The tests, reported at test_level: statistic, testing no break against $k$ breaks for every $k = 1,\ldots,m$ , with its critical_values; statistic_type, "SupLR" or "SupF", and NA when a requested robust test is unavailable; wdmax and wdmax_critical_values; the sequential tests of $l$ against $l+1$ breaks, each containing l, a statistic and its critical_values; and the number of changing_parameters, which includes the changing covariance parameters when robust = "none".
br_selected: The outcome of the break-number determination at test_level: the selected number of breaks, the WDmax statistic with its critical value and significance flag, and the sequential steps taken. breaks is 0 when WDmax is not significant, and NA when the tests are unavailable for the requested specification.
estimation: The estimates related to the selected number of breaks: estimated breaks; their confidence intervals ci_breaks; coefficients by regimes and their confidence intervals; disturbance covariance matrices. This component is NULL when no break is detected, in which case only testing and br_selected are informative.
y: The responses used in estimation, rows spec$y_rows of data.

References

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59(3), 817–858.

Andrews, D. W. K., and Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60(4), 953–966.

Bai, J., and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47–78.

Qu, Z., and Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica, 75(2), 459–502.

Examples

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)

fit <- sysbreak(cbind(y1, y2) ~ x, data = dat, m = 1, trim = 0.2)
fit$estimation$breaks

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)

fit <- sysbreak(cbind(y1, y2) ~ x, data = dat, m = 1, trim = 0.2)
fit$estimation$breaks

Methods for Displaying Structural-Break Fits

Description

Fits returned by sysbreak, varbreak and netbreak. All refer to the estimates at the selected number of breaks.

Usage

## S3 method for class 'sysbreak'
coef(object, ...)

## S3 method for class 'sysbreak'
vcov(object, ...)

## S3 method for class 'sysbreak'
confint(object, parm, level = NULL, type = c("breaks", "coef"), ...)

## S3 method for class 'sysbreak'
residuals(object, ...)

## S3 method for class 'sysbreak'
fitted(object, ...)

## S3 method for class 'sysbreak'
nobs(object, ...)
## S3 method for class 'sysbreak'
coef(object, ...)

## S3 method for class 'sysbreak'
vcov(object, ...)

## S3 method for class 'sysbreak'
confint(object, parm, level = NULL, type = c("breaks", "coef"), ...)

## S3 method for class 'sysbreak'
residuals(object, ...)

## S3 method for class 'sysbreak'
fitted(object, ...)

## S3 method for class 'sysbreak'
nobs(object, ...)

Arguments

object

A fit returned by sysbreak(), varbreak() or netbreak().

...

Not used.

parm

Breaks (type = "breaks") or coefficients (type = "coef") to report, as indices or row names.

level

Coverage probability. By default the ci_level of the fit, the level of the intervals shown by print() and summary(). For break dates either 0.95 or 0.90, the two levels computed at estimation; for coefficients any value in $(0, 1)$ .

type

"breaks" for the break dates or "coef" for the regression coefficients.

Value

coef: A named vector of the regime coefficients: all coefficients of regime 1, then those of regime 2, and so on. Each name joins the regime and the coefficient label used by summary(), as in "regime1:y1:x" (equation y1, regressor x) or "regime2:mu:node3" for netbreak. Coefficients held constant by coef_breaks are repeated in every regime.
vcov: The covariance matrix of coef(), with rows and columns in the same order and with the same names. When coef_breaks holds coefficients constant, the matrix is singular, since the repeated entries of a constant coefficient are perfectly correlated.
confint: For type = "breaks", a matrix with one row per break: the lower bound, the estimated break date and the upper bound. For type = "coef", the lower and upper bounds of confidence intervals, estimate $\pm$ normal quantile times standard error, treating the break dates as known.
residuals, fitted: Matrices with one column per equation and one row per observation; the row names are the rows of the data (spec$y_rows).
nobs: The number of observations used.

When no break is selected the regime estimates are not computed, and all but nobs stop with an error.

Examples

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)
fit <- sysbreak(cbind(y1, y2) ~ x, dat, m = 1, trim = 0.3)

coef(fit)
confint(fit)
confint(fit, level = 0.90)
confint(fit, type = "coef")
head(residuals(fit))
nobs(fit)

set.seed(11)
bigt <- 40
x <- rnorm(bigt)
y1 <- 1 + 0.4 * x + rnorm(bigt, sd = 0.3)
y2 <- -0.5 + 0.2 * x + rnorm(bigt, sd = 0.3)
y1[21:40] <- y1[21:40] + 1.2 - 0.6 * x[21:40]
y2[21:40] <- y2[21:40] - 0.8 + 0.4 * x[21:40]
dat <- data.frame(y1 = y1, y2 = y2, x = x)
fit <- sysbreak(cbind(y1, y2) ~ x, dat, m = 1, trim = 0.3)

coef(fit)
confint(fit)
confint(fit, level = 0.90)
confint(fit, type = "coef")
head(residuals(fit))
nobs(fit)

Structural Breaks in a VAR

Description

Estimation of a VAR affected by structural breaks in the regression coefficients and/or the variance covariance matrix of the residuals.

Usage

varbreak(y, lags, m, intercept = TRUE, coef_breaks = "all",
  test_level = 0.05, ci_level = 0.95,
  trim = 0.15, verbose = FALSE, brv = FALSE,
  robust = c("none", "hc", "hac"), hetq = FALSE, prewhit = FALSE,
  restart = c("none", "brbp", "brbp_residual"),
  restart_B = 10, restart_verbose = FALSE, h = NULL)
varbreak(y, lags, m, intercept = TRUE, coef_breaks = "all",
  test_level = 0.05, ci_level = 0.95,
  trim = 0.15, verbose = FALSE, brv = FALSE,
  robust = c("none", "hc", "hac"), hetq = FALSE, prewhit = FALSE,
  restart = c("none", "brbp", "brbp_residual"),
  restart_B = 10, restart_verbose = FALSE, h = NULL)

Arguments

y

Numeric response matrix with one column per variable.

lags

Positive integer, number of lags.

m

Integer, maximum number of breaks allowed.

intercept

Logical. If TRUE, include an intercept in the regressors matrix.

coef_breaks

Coefficient-break selector, applied after the VAR lag matrix is built. The default "all" lets all VAR coefficients change. Use "none" or NULL for no coefficient changes, for which brv = TRUE is required so that the covariance matrix of the residuals can change. Use a list such as list(y1 ~ ., y2 ~ 0) to restrict breaks to selected regression coefficients.

test_level

ci_level

Coverage probability of the reported confidence intervals for the break dates. Either 0.95 or 0.90.

trim

verbose

Logical. If TRUE, print additional progress information from the testing and estimation.

brv

Logical. If TRUE, allow the disturbance covariance matrix to change across regimes.

robust

hetq

Logical. If TRUE, allow regressor moments to vary across regimes when computing confidence intervals for break dates.

prewhit

Logical. If TRUE, prewhiten the scores by a VAR(1) before the HAC estimation (Andrews and Monahan, 1992). Used only when robust = "hac".

restart

restart_B

Integer, number of restart values used when restart != "none".

restart_verbose

Logical. If TRUE, print restart progress.

h

Optional positive integer for forecast horizon. If supplied, attach Diebold–Yilmaz generalized spillover measures in spillover.

Details

The interpretation of testing$statistic depends on robust.

robust = "none" gives the SupLR statistic. The code can test the coefficients specified by coef_breaks, the disturbance covariance when brv = TRUE, or both.
robust = "hc" or "hac" gives the robust SupF statistic, for the coefficients only, because the covariance-break critical values are case dependent under heteroskedasticity or serial correlation; it assumes a constant error covariance. With brv = TRUE, the estimates, standard errors and confidence intervals account for the covariance breaks; under "hc" the intervals further require errors without ARCH-type dependence.

Value

An object of class c("varbreak", "sysbreak") containing:

spec: A summary of the setup, including the sample size bigt, the number of equations n, the total number of coefficients per regime q, the arguments m, lags, intercept, trim, brv, robust, hetq, prewhit, test_level and ci_level, the equation and coefficient names, the retained input rows y_rows after discarding the lags, and the coef_breaks selector.
testing: The tests, reported at test_level: statistic, testing no break against $k$ breaks for every $k = 1,\ldots,m$ , with its critical_values; statistic_type, "SupLR" or "SupF", and NA when a requested robust test is unavailable; wdmax and wdmax_critical_values; the sequential tests of $l$ against $l+1$ breaks, each containing l, a statistic and its critical_values; and the number of changing_parameters, which includes the changing covariance parameters when robust = "none".
br_selected: The outcome of the break-number determination at test_level: the selected number of breaks, the WDmax statistic with its critical value and significance flag, and the sequential steps taken. breaks is 0 when WDmax is not significant, and NA when the tests are unavailable for the requested specification.
estimation: The estimates related to the selected number of breaks: estimated breaks; their confidence intervals ci_breaks; coefficients by regimes and their confidence intervals; disturbance covariance matrices. This component is NULL when no break is detected, in which case only testing and br_selected are informative.
spillover: When h is supplied and at least one break is selected, regime-specific Diebold–Yilmaz generalized spillover measures returned by dyspill.
y: The responses used in estimation, rows spec$y_rows of y.

Note that m is the maximum number of breaks allowed. Testing output is reported for every value from 1 through m, while estimation corresponds to the number of breaks selected by the procedure under test_level. The optional spillover component is omitted when h = NULL. The fit has print(), summary(), plot() and the accessors in sysbreak-methods.

References

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59(3), 817–858.

Andrews, D. W. K., and Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60(4), 953–966.

Bai, J., and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47–78.

Qu, Z., and Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica, 75(2), 459–502.

Examples

set.seed(12)
bigt <- 45
y <- matrix(0, bigt, 2)
for (tt in 2:bigt) {
  shift <- if (tt > 24) c(0.8, -0.6) else c(0, 0)
  y[tt, ] <- shift +
    c(0.3 * y[tt - 1, 1], -0.2 * y[tt - 1, 2]) +
    rnorm(2, sd = 0.3)
}

fit <- varbreak(y, lags = 1, m = 1, trim = 0.2)
fit$estimation$breaks

set.seed(12)
bigt <- 45
y <- matrix(0, bigt, 2)
for (tt in 2:bigt) {
  shift <- if (tt > 24) c(0.8, -0.6) else c(0, 0)
  y[tt, ] <- shift +
    c(0.3 * y[tt - 1, 1], -0.2 * y[tt - 1, 2]) +
    rnorm(2, sd = 0.3)
}

fit <- varbreak(y, lags = 1, m = 1, trim = 0.2)
fit$estimation$breaks

Package 'sysbreak'

Help Index

Methods to Examine What Changes at Each Break Date

Description

Usage

Arguments

Details

Value

References

Examples

GAUSS/MATLAB Example Data 1

Description

Usage

Format

Source

GAUSS/MATLAB Example Data 2

Description

Usage

Format

Source

Diebold-Yilmaz Spillover Measures Without Breaks

Description

Usage

Arguments

Value

Examples

Diebold-Yilmaz Generalized Spillover Measures

Description

Usage

Arguments

Details

Value

References

Examples

U.S. House Prices and the Macroeconomy

Description

Usage

Format

Source

References

International Inflation

Description

Usage

Format

Source

References

Structural Breaks in a network VAR

Description

Usage

Arguments

Details

Value

References

Examples

Simulated Network VAR

Description

Usage

Format

Details

Source

References

Ordered Structural Breaks in a System of Equations

Description

Usage

Arguments

Details

Value

References

Examples

Coefficient Layout of an Ordered-Break Specification

Description

Usage

Arguments

Value

Examples

Plot a Structural-Break Fit

Description

Usage

Arguments

Value