Help for package mbreaks

Type:

Package

Title:

Estimation and Inference for Structural Breaks in Linear Regression Models

Version:

1.0.1

Description:

Functions provide comprehensive treatments for estimating, inferring, testing and model selecting in linear regression models with structural breaks. The tests, estimation methods, inference and information criteria implemented are discussed in Bai and Perron (1998) "Estimating and Testing Linear Models with Multiple Structural Changes" <doi:10.2307/2998540>.

URL:

https://github.com/RoDivinity/mbreaks

BugReports:

https://github.com/RoDivinity/mbreaks/issues

License:

MIT + file LICENSE

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.2.3

Depends:

R (≥ 3.3)

Imports:

ggplot2

Suggests:

knitr, rmarkdown, graphics, testthat

VignetteBuilder:

knitr, rmarkdown

NeedsCompilation:

Packaged:

2024-11-11 07:44:34 UTC; linhnguyen

Author:

Linh Nguyen [aut, cre], Yohei Yamamoto [aut], Pierre Perron [aut]

Maintainer:

Linh Nguyen <nguye535@purdue.edu>

Repository:

CRAN

Date/Publication:

2024-11-11 11:40:02 UTC

Format output of n break model

Description

compile_model() compiles the information of model class object x into three main tables:

date_tab: Table for estimated break date in the model with 90% and 95% confidence intervals based on robust,hetomega, hetq options for errors and prewhit option.
RS_tab: Table for estimated coefficients for z regressors with corrected standard errors based on robust,hetdat,hetvar options for errors and prewhit option.
FS_tab: Table for estimated coefficients for x regressors with corrected standard errors based on robust, hetdat, and hetvar options for errors and prewhit option.

Usage

compile_model(x, digits = 3)

Arguments

x

the model class to format

digits

number of digits displayed in console. Default value is 3

Value

Formatted x with the following appended tables:

'date_tab': A data frame storing the break date estimated by the model, and their corresponding confidence intervals.
'RS_tab': A data frame storing the estimated coefficients which allowed to change across regimes with corrected standard errors.
'FS_tab': A data frame storing the estimated coefficients which is constant across regimes with corrected standard errors.

Note

If x returns 0 number of estimated break, the function will return NULL value instead of the list in Value.
If x is a pure structural break, the 'FS_tab' will return NULL in Value.

Compile the Output of Sup Wald Test

Description

'compile_sbtests' formats the output of 'sbtests' into two tables.

Usage

compile_sbtests(x, digits = 3)

Arguments

x

An 'sbtests' class object.

digits

The number of decimal places displayed.

Value

A modified 'sbtests' object, 'x', with two appended data frames:

supF1: A data frame containing SupF test statistics for testing 0 versus m breaks, where m is the maximum number of breaks considered in 'x'. It includes critical values at the 10%, 5%, 2.5%, and 1% levels.
UDMax: A data frame containing Double Max test statistics with critical values at the 10%, 5%, 2.5%, and 1% levels.

Compile the output of sequential Sup Wald test

Description

'compile_seqtests' formats the output of the 'seqtests' class object to 1 table

'sfl': A table containing sequential sup F tests statistics of 'l' versus 'l+1' for 'l' in '1' to 'm' breaks with critical values of the corresponding tests at 1%, 2.5%, 5%, and 10% significance levels.

Usage

compile_seqtests(x)

Arguments

x

'seqtests' class object

Value

class 'seqtests' list 'x' with appended data frame 'sfl' containing the sequential SupF test statistics with critical values at 10%, 5%, 2.5%, and 1% level.

Heteroskedasticy and autocorrelation consistency correction for residuals

Description

'hac()' corrects the estimated errors based on options of prewhitening using a AR(1) process estimation of error terms to obtain heteroskedasticy and autocorrelation consistency (HAC) errors with automatic bandwith and kernel similar to Andrews, 1994

Usage

correct(reg, res, prewhit)

Arguments

reg

matrix of regressors

res

matrix of estimated residuals

prewhit

Option of using prewhitening process. If 1, an AR(1) process will be used to filter. If 0, skipped the filtering process

Value

hac Heteroskedasticy and autocorrelation consistent errors

Computation of global minimizer for pure structural change model

Description

'dating()' computes break points that globally minimizes SSR via dynamic programming approach. To avoid recursion depth increases as number of breaks in the model increases, a temporary array is used to store optimal partition with corresponding SSR for all permissible subsamples for all 1:m-1 breaks. For the m-th break, the problem becomes finding where to insert the last feasible m+1-th segment into the sample partitioned by m-1 breaks to obtain minimum SSR over the sample

Usage

dating(y, z, h, m, q, bigT)

Arguments

y

matrix of dependent variable

z

matrix of regressors with coefficients allowed to change across regimes

h

minimum length of segment

m

maximum number of breaks

q

number of 'z' regressors

bigT

sample period T

Value

A list containing the following components:

glb

minimum global SSR

datevec

Vector of dates (optimal minimizers)

bigvec

Associated SSRs

Diagonal partition given break dates

Description

'diag_par()' partition the matrix of 'z' regressors which coefficients are changed based on the provided break dates

Usage

diag_par(input, m, date)

Arguments

input

matrix of independent variables z with coefficients allowed to change overtime

m

number of breaks in the series

date

vector of break dates

Value

output: matrix of partitioned variables corresponds to break dates

Examples

z = matrix(c(1:100),50,2)
m = 2  #2 breaks
date = matrix(c(15,30),2,1) #first break at t = 15; second break at t = 30
diag_par(z,m,date)

Estimate a model with pre-specified number of breaks

Description

'dofix()' compute a structural change model with pre-specified number of breaks.

Usage

dofix(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  fixn = 5,
  eps = 1e-05,
  eps1 = 0.15,
  maxi = 10,
  fixb = 0,
  betaini = 0,
  printd = 0,
  prewhit = 1,
  robust = 1,
  hetdat = 1,
  hetvar = 1,
  hetq = 1,
  hetomega = 1,
  const = 1,
  h = NULL
)

Arguments

y_name

name of dependent variable in the data set

z_name

name of independent variables in the data set which coefficients are allowed to change across regimes. default is vector of 1 (Mean-shift model)

x_name

name of independent variables in the data set which coefficients are constant across regimes. default is 'NULL'

data

name of data set used

fixn

number of breaks specified

eps

convergence criterion for iterative recursive computation

eps1

value of trimming (in percentage) for the construction and critical values. Minimal segment length 'h' will be set at default = int(eps1*T) (T is total sample size).

eps1 = 0.05 Maximal value of m = 10.
eps1 = 0.10 Maximal value of m = 8.
eps1 = 0.15 Maximal value of m = 5.
eps1 = 0.20 Maximal value of m = 3.
eps1 = 0.25 Maximal value of m = 2.
eps1=0 This option allows users to explicitly specify minimum segment length 'h' parameters.

maxi

maximum number of iterations

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial beta_0 to use in estimation

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

prewhit

set to 1 to apply AR(1) prewhitening prior to estimating the long run covariance matrix.

robust

set to 1 to allow for heterogeneity and autocorrelation in the residuals, 0 otherwise. The method used is Andrews(1991) automatic bandwidth with AR(1) approximation with quadratic kernel. Note: Do not set to 1 if lagged dependent variables are included as regressors.

hetdat

option for the construction of the F tests. Set to 1 if want to allow different moment matrices of the regressors across segments. If hetdat = 0, the same moment matrices are assumed for each segment and estimated from the ful sample. It is recommended to set hetdat=1 if number of regressors x > 0.

hetvar

option for the construction of the F tests.Set to 1 if users want to allow for the variance of the residuals to be different across segments. If hetvar=0, the variance of the residuals is assumed constant across segments and constructed from the full sample. hetvar=1 when robust =1)

hetq

used in the construction of the confidence intervals for the break dates. If hetq=0, the moment matrix of the data is assumed identical across segments

hetomega

used in the construction of the confidence intervals for the break dates. If hetomega=0, the long run covariance matrix of zu is assumed identical across segments (the variance of the errors u if robust=0).

const

indicates whether the regression model include an intercept changing across regimes. Default value is 1

h

Minimum segment length of regime considered in estimation. If users want to specify a particular value, please set 'eps1=0'

Value

out A list of class 'model' contains all information about the estimated structural change model with 'fixn' breaks

Examples

dofix('rate',data=real,fixn=3)

Global SSR minimizer for structural change model

Description

'doglob()' identify if the structural change model is i) pure or ii) partial change model. The procedure then calls appropriate functions dating to estimate the pure change model and nldat to estimate the partial change model.

Usage

doglob(y, z, x, m, eps, h, maxi, fixb, betaini, printd, eps1)

Arguments

y

matrix of dependent variable

z

matrix of independent variables with coefficients allowed to change across regimes

x

matrix of independent variables with coefficients constant across regimes

m

number of breaks in the structural change model

eps

convergence criterion for iterative recursive computation. (For partial change model ONLY)

h

Minimum segment length of regime considered in estimation. If users want to specify a particular value, please set 'eps1=0'

maxi

maximum number of iterations. (For partial change model ONLY)

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial beta_0 to use in estimation (Must be a 'p x 1' matrix, where p is number of x variables)

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

eps1

trimming level

Value

A list containing the following components:

glb: Minimum global SSR.
datevec: Vector of dates (optimal minimizers).
bigvec: Associated SSRs with possible break dates combination.

Estimating number of breaks via information criterion

Description

'doorder()' estimates the number of breaks using one of the following information criteria:

modified Bayesian information criterion by Kurozumi and Tuvaandorj, 2011,
modified Schwarz information criterion by Liu, Wu and Zidek, 1997,
Bayesian information criterion by Yao, 1988

and the structural break model corresponding to estimated number of breaks.

Usage

doorder(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  m = 5,
  eps = 1e-05,
  eps1 = 0.15,
  maxi = 10,
  fixb = 0,
  betaini = 0,
  printd = 0,
  ic = "KT",
  const = 1,
  h = NULL,
  prewhit = 1,
  hetdat = 1,
  hetq = 1,
  hetomega = 1,
  hetvar = 1,
  robust = 1
)

Arguments

y_name

name of dependent variable in the data set

z_name

name of independent variables in the data set which coefficients are allowed to change across regimes. default is vector of 1 (Mean-shift model)

x_name

name of independent variables in the data set which coefficients are constant across regimes. default is 'NULL'

data

name of data set used

m

maximum number of breaks

eps

convergence criterion for iterative recursive computation

eps1

value of trimming (in percentage) for the construction and critical values. Minimal segment length 'h' will be set at default = int(eps1*T) (T is total sample size). There are five options:

'eps1=0.05' Maximal value of 'm' = 10.
'eps1=0.10' Maximal value of 'm' = 8.
'eps1=.15' Maximal value of 'm' = 5.
'eps1=.20' Maximal value of 'm' = 3.
'eps1=.25' Maximal value of 'm' = 2.
'eps1=0' This option allows users to explicitly specify minimum segment length 'h' parameters

maxi

maximum number of iterations

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial beta_0 to use in estimation

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

ic

indicator which information criterion is used in selecting number of breaks:

KT
BIC
LWZ

The default value is KT

const

indicates whether the regression model include an intercept changing across regimes. Default value is 1

h

Minimum segment length of regime considered in estimation. If users want to specify a particular value, please set 'eps1=0'

prewhit

set to 1 to apply AR(1) prewhitening prior to estimating the long run covariance matrix.

hetdat

hetq

used in the construction of the confidence intervals for the break dates. If hetq=0, the moment matrix of the data is assumed identical across segments

hetomega

hetvar

robust

Value

A list of class 'model' that contains one of the following:

mBIC: change model with number of breaks selected by BIC
mLWZ: change model with number of breaks selected by LWZ
mKT: change model with number of breaks selected by KT

References

Liu J, Wu S, Zidek JV (1997). "On Segmented Multivariate Regressions", Statistica Sinica, 7, 497-525. Yao YC (1988). "Estimating the Number of Change-points via Schwartz Criterion", Statistics and Probability Letters, 6, 181-189. Kurozumi E, Tuvaandorj P (2011). "Model Selection Criteria in Multivariate Models with Multiple Structural Changes", Journal of Econometrics 164, 218-238.

Examples

doorder('rate',data=real,ic=c('BIC'))

Estimating number of breaks using repartition procedure

Description

'dorepart()' computes the repartition estimates of the breaks obtained by the sequential method by Bai, 1995. It allows estimates that have the same asymptotic distribution as those obtained by global minimization. Otherwise, the output from the procedure "estim" below does not deliver asymptotically correct confidence intervals for the break dates.

Usage

dorepart(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  m = 5,
  eps = 1e-05,
  eps1 = 0.15,
  maxi = 10,
  fixb = 0,
  betaini = 0,
  printd = 0,
  prewhit = 1,
  robust = 1,
  hetdat = 1,
  hetvar = 1,
  const = 1,
  signif = 2
)

Arguments

y_name

name of dependent variable in the data set

z_name

name of independent variables in the data set, whose coefficients are allowed to change across regimes. default is a vector of 1 (Mean-shift model).

x_name

name of independent variables in the data set whose coefficients are constant across regimes. default is NULL.

data

name of the data set used

m

Maximum number of structural changes allowed. If not specified, m will be set to default value matching the eps1 input

eps

convergence criterion for iterative recursive computation

eps1

value of trimming (in percentage) for the construction and critical values. Minimal segment length h will be set at default = int(eps1 * T) (T is total sample size). There are five options:

eps1 = 0.05 Maximal value of m = 10.
eps1 = 0.10 Maximal value of m = 8.
eps1 = 0.15 Maximal value of m = 5.
eps1 = 0.20 Maximal value of m = 3.
eps1 = 0.25 Maximal value of m = 2.
eps1 = 0 This option is not allowed.

maxi

maximum number of iterations

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial \beta_0 to use in estimation

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

prewhit

set to 1 to apply AR(1) prewhitening prior to estimating the long run covariance matrix.

robust

hetdat

option for the construction of the F tests. Set to 1 if you want to allow different moment matrices of the regressors across segments. If hetdat = 0, the same moment matrices are assumed for each segment and estimated from the full sample. It is recommended to set hetdat = 1 if number of regressors x > 0.

hetvar

option for the construction of the F tests. Set to 1 if users want to allow for the variance of the residuals to be different across segments. If hetvar = 0, the variance of the residuals is assumed constant across segments and constructed from the full sample. hetvar = 1 when robust = 1

const

indicates whether the regression model includes an intercept changing across regimes. Default value is 1

signif

significance level used to sequential test to select number of breaks.

4: 1% level
3: 2.5% level
2: 5% level
1: 10% level

Value

A list of class model for the structural break model estimated by the repartition procedure.

References

Bai, J. 1995, "Estimating Breaks One at a Time", Econometric Theory, 13, 315-352

Examples

dorepart('inf', 'inflag', 'inffut', data = nkpc)

Sequential Sup F tests

Description

'doseqtests()' computes the sequential sup F tests of l versus l+1 for l from 1 to m with each corresponding null hypothesis of maximum number of break is l and alternative hypothesis is l+1. The l breaks under the null hypothesis are taken from the global minimization estimation

Usage

doseqtests(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  m = 5,
  eps = 1e-05,
  eps1 = 0.15,
  maxi = 10,
  fixb = 0,
  betaini = 0,
  printd = 0,
  prewhit = 1,
  robust = 1,
  hetdat = 1,
  hetvar = 1,
  hetq = 1,
  hetomega = 1,
  const = 1
)

Arguments

y_name

name of dependent variable in the data set

z_name

name of independent variables in the data set which coefficients are allowed to change across regimes. default is a vector of 1 (Mean-shift model)

x_name

name of independent variables in the data set which coefficients are constant across regimes. default is 'NULL'

data

name of data set used

m

maximum number of breaks

eps

convergence criterion for recursive calculations (For partial change model ONLY)

eps1

value of trimming (in percentage) for the construction and critical values. Minimal segment length 'h' will be set at default = int(eps1*T) (T is total sample size). There are five options:

'eps1=0.05' Maximal value of 'm' = 10.
'eps1=0.10' Maximal value of 'm' = 8.
'eps1=.15' Maximal value of 'm' = 5.
'eps1=.20' Maximal value of 'm' = 3.
'eps1=.25' Maximal value of 'm' = 2.
'eps1=0' is not allowed. The test is undefined for no trimming level.

maxi

number of maximum iterations for recursive calculations of finding global minimizers.default = 10 (For partial change model ONLY)

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial beta_0 to use in estimation (Must be a 'p x 1' matrix, where p is number of x variables)

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

prewhit

set to 1 to apply AR(1) prewhitening prior to estimating the long run covariance matrix.

robust

hetdat

hetvar

hetq

used in the construction of the confidence intervals for the break dates. If hetq=0, the moment matrix of the data is assumed identical across segments

hetomega

const

indicates whether the regression model include an intercept changing across regimes. Default value is 1

Value

A list that contains following:

supfl: SupF(l+1|l) test statistics.
cv: Critical values for SupF(l+1|l) test.

Examples

doseqtests('inf',c('inflag','lbs','inffut'),data=nkpc,prewhit=0)

Estimating number of breaks using sequential tests

Description

'dosequa()' sequentially increases the number of breaks from '1' to 'm' until the sequential tests reject and estimate the structural change model with corresponding estimated breaks. The procedure is proposed by Bai and Perron, 1998.

Usage

dosequa(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  m = 5,
  eps = 1e-05,
  eps1 = 0.15,
  maxi = 10,
  fixb = 0,
  betaini = 0,
  printd = 0,
  prewhit = 1,
  robust = 1,
  hetdat = 1,
  hetvar = 1,
  hetq = 1,
  hetomega = 1,
  const = 1,
  signif = 2
)

Arguments

y_name

name of dependent variable in the data set

z_name

name of independent variables in the data set, which coefficients are allowed to change across regimes. Default value is vector of 1 (Mean-shift model).

x_name

name of independent variables in the data set, which coefficients are constant across regimes. Default value is NULL.

data

name of the data set used

m

maximum number of breaks

eps

convergence criterion for iterative recursive computation

eps1

value of trimming (in percentage) for the construction and critical values. Minimal segment length 'h' will be set at default value = int(eps1 * T) (T is total sample size). There are five options:

eps1 = 0.05 Maximal value of m = 10.
eps1 = 0.10 Maximal value of m = 8.
eps1 = 0.15 Maximal value of m = 5.
eps1 = 0.20 Maximal value of m = 3.
eps1 = 0.25 Maximal value of m = 2.
eps1 = 0 This option is not allowed.

maxi

maximum number of iterations

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial \beta_0 to use in estimation

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

prewhit

set to 1 to apply AR(1) prewhitening prior to estimating the long run covariance matrix.

robust

hetdat

hetvar

option for the construction of the F tests. Set to 1 if users want to allow for the variance of the residuals to be different across segments. If hetvar = 0, the variance of the residuals is assumed constant across segments and constructed from the full sample. hetvar = 1 when robust = 1

hetq

used in the construction of the confidence intervals for the break dates. If hetq = 0, the moment matrix of the data is assumed identical across segments.

hetomega

used in the construction of the confidence intervals for the break dates. If hetomega = 0, the long run covariance matrix of zu is assumed identical across segments (the variance of the errors u if robust = 0).

const

indicates whether the regression model includes an intercept changing across regimes. Default value is 1

signif

significance level used in the sequential test to select number of breaks.

4: 1% level
3: 2.5% level
2: 5% level
1: 10% level

Value

A list of 'model' class with the number of breaks selected by sequential tests.

Examples

dosequa('rate', data = real, signif = 1)

SupF, UDMax & WDMax testing procedure

Description

'dotest()' compute the test statistics and report the critical values of the 2 main supF tests below:

SupF test of 0 vs m breaks
Double Max test proposed by Perron and Bai, 1998

Usage

dotest(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  m = 5,
  eps = 1e-05,
  eps1 = 0.15,
  maxi = 10,
  fixb = 0,
  betaini = 0,
  printd = 0,
  prewhit = 1,
  robust = 1,
  hetdat = 1,
  hetvar = 1,
  hetq = 1,
  hetomega = 1,
  const = 1
)

Arguments

y_name

matrix of dependent variable

z_name

matrix of regressors which coefficients are allowed to change across regimes.

x_name

matrix of regressors which coefficients are constant across regimes.

data

the data set for estimation

m

maximum number of breaks

eps

convergence criterion for iterative recursive computation

eps1

trimming level

maxi

maximum number of iterations

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial beta_0 to use in estimation (Must be a 'p x 1' matrix, where p is number of x variables)

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

prewhit

option to use AR(1) for prewhitening

robust

hetdat

hetvar

hetq

used in the construction of the confidence intervals for the break dates. If hetq=0, the moment matrix of the data is assumed identical across segments

hetomega

const

indicates whether the regression model include an intercept changing across regimes. Default value is 1

Value

A list that contains following:

ftest: SupF test of 0 vs m (1 to maximum) breaks statistics
cv_supF: Critical values for Sup F test
cv_Dmax: Critical values for Double Max test
supF1: table summarizing the SupF test (for viewing purposes)
UDMax: table summarizing the Double Max test (including UDMax statistics and CVs)

Structural change model estimation

Description

'estim()' estimates the structural change model by OLS given specified vector of break dates It also computes and reports confidence intervals for the break dates based on asymptotic distributions of break date and corrected standard errors of coefficients estimates given the structure of covariance matrix for model errors by specifying error options 'robust', 'hetomega', 'hetq', 'hetdat' and 'hetvar'

Usage

estim(m, q, z, y, b, robust, prewhit, hetomega, hetq, x, p, hetdat, hetvar)

Arguments

m

number of breaks

q

number of 'z' regressors z

z

matrix of regressors with coefficients are allowed to change across regimes

y

matrix of dependent variable

b

vector of break dates

robust, hetomega, hetq, hetdat, hetvar

options for assumptions on the error terms. For more details, please refer to mdl.

prewhit

option to use prewhitening process based on AR(1) approximation

x

matrix of regressors with coefficients are constant across regimes

p

number of regressors x

Value

A list containing the following components:

date: List of estimated breaks.
CI: List of Confidence Intervals for each corresponding break.
beta: Estimated coefficients of the regression. The first (m+1)*q are coefficients of q variables z that change across regimes. The last p are coefficients of p variables x that are constant across regimes.
SE: Corrected standard errors for the coefficients' estimates

Estimatd break confidence interval

Description

'interval()' computes confidence intervals for the break dates based on approximating the limiting distribution of the break date following the "shrinking shifts" asymptotic framework

Usage

interval(y, z, zbar, b, q, m, robust, prewhit, hetomega, hetq, x, p)

Arguments

y

matrix of dependent variable

z

matrix of independent variables with coefficients allowed to change across regimes

zbar

partitioned matrix of independent variables with coefficients allowed to change across regimes according to break date vector 'b'

b

vector of break breaks

q

number of 'z' regressors

m

maximum number of breaks

robust

set to 1 to allow for heterogeneity and autocorrelation in the residuals, 0 otherwise. The method used is Andrews(1991) automatic bandwidth with AR(1) approximation with quadratic kernel. Note: Do not set to 1 if lagged dependent variables are included as regressors.

prewhit

Option of using prewhitening process. If 1, an AR(1) process will be used to filter. If 0, skipped the filtering process

hetomega, hetq

options for assumptions of error terms structure. For more details, refers to [mdl()]

x

matrix of independent variables with coefficients constant across regimes

p

number of 'x' regressors

Value

bound Confidence intervals of break date in 90% and 95% significant level

Comprehensive structural change estimation and testing

Description

'mdl()' calls main functions of the 'mbreaks' package to execute the following estimation procedures:

'dotest()': Function dotest conducts Sup F tests of '0' versus 'm' breaks and Double Max tests.
'doseqtests()': Function doseqtests conducts the sequential Sup F tests of 'l' versus 'l+1' breaks.
'doorder()': Function doorder conducts the number of breaks selection from '1' to 'm' breaks using the following information critera: KT,BIC, and LWZ.
'dosequa()': Function dosequa conducts the number of breaks selection by sequential tests from '1' to 'm' breaks using sequential Sup F tests.
'dofix()': Function dofix conducts structural break model estimation with 'fixn' breaks.

All the procedures automatically identify if the 'model' is either i) pure structural breaks model or ii) partial structural breaks model

Usage

mdl(
  y_name,
  z_name = NULL,
  x_name = NULL,
  data,
  eps1 = 0.15,
  m = 5,
  prewhit = 1,
  robust = 1,
  hetdat = 1,
  hetvar = 1,
  hetomega = 1,
  hetq = 1,
  maxi = 10,
  eps = 1e-05,
  fixn = -1,
  fixb = 0,
  betaini = 0,
  printd = 0,
  const = 1,
  signif = 2,
  h = NULL
)

Arguments

y_name

name of dependent variable in the data set.

z_name

name of independent variables in the data set which coefficients are allowed to change across regimes. default is vector of 1 (Mean-shift model).

x_name

name of independent variables in the data set which coefficients are constant across regimes. default is NULL.

data

the data set for estimation.

eps1

value of trimming (in percentage) for the construction and critical values. Minimal segment length 'h' will be set at default = int(eps1*T) (T is total sample size).

eps1 = 0.05 Maximal value of m = 10.
eps1 = 0.10 Maximal value of m = 8.
eps1 = 0.15 Maximal value of m = 5.
eps1 = 0.20 Maximal value of m = 3.
eps1 = 0.25 Maximal value of m = 2.
eps1 = 0 This option allows users to explicitly specify minimum segment length 'h' parameters. However, this option will not be allowed for testing and testing related functions.

The default value is set at eps1 = 0.15.

m

Maximum number of structural changes allowed. If not specify, m will be set to default value matching 'eps1' input.

prewhit

set to 1 to apply AR(1) prewhitening prior to estimating the long run covariance matrix.

robust

hetdat

hetvar

hetomega

hetq

used in the construction of the confidence intervals for the break dates. If hetq=0, the moment matrix of the data is assumed identical across segments

maxi

number of maximum iterations for recursive calculations of finding global minimizers.default = 10 (For partial change model ONLY).

eps

convergence criterion for recursive calculations (For partial change model ONLY)

fixn

number of pre-specified breaks. default = -1. It will be replaced automatically to 2 if no specification is given (For partial change model ONLY)

fixb

option to use fixed initial input \beta. If 1, the model will use values given in betaini. If 0, betaini is skipped

betaini

Initial \beta_0 to use in estimation (Must be a 'p x 1' matrix, where 'p' is number of x variables)

printd

Print option for model estimation. default = 0, to suppress intermediate outputs printing to console

const

indicates whether the regression model include an intercept changing across regimes. Default value is 1.

signif

significance level used to sequential test to select number of breaks.

4: 1% level
3: 2.5% level
2: 5% level
1: 10% level

h

Minimum segment length of regime considered in estimation. If users want to specify a particular value, please set 'eps1=0'

Value

A list that contains the following:

sbtests: A list of class 'sbtests' representing Sup F tests of 0 versus m breaks and Double Max tests.
seqtests: A list of class 'seqtests' representing sequential Sup F test of l versus l+1 breaks.
BIC: A list of class 'model' with structural break model estimated by number of breaks by BIC criterion.
LWZ: A list of class 'model' with structural break model estimated by number of breaks by LWZ criterion.
KT: A class 'model' with structural break model estimated by number of breaks by KT criterion.
sequa: A class 'model' with structural break model estimated by number of breaks by sequential tests.
fix: A class 'model' with structural break model estimated by pre-specified 'fixn' number of breaks.

Note: All default values of error assumptions (robust, hetdat, hetvar, hetq) are set to 1. The implications on the structure of model\'s errors related to individual settings are explained within the arguments section for each option.

Examples

 US_rate = mdl('rate',data=real)
 nkpc_lbs = mdl('inf',c('inflag','lbs','inffut'),data=nkpc,prewhit = 0)

New Keynesian Phillips curve data

Description

Data set from inflation and other macroeconomic variables

Usage

nkpc

Format

## 'nkpc' A data frame with 151 rows and 12 columns:

year: Current period year
quarter: Quarter in current period year
inf: Inflation rate
inflag: Inflation rate in previous period
inffut: Expected inflation rate, taken as value of inflation rate of next period
ygap: Productivity output gap
lbs
lbslag
spreadlag
dwlag
dcplag

Source

Perron, P. and Yamamoto, Y., 2015. "Using ols to estimate and test for structural changes in models with endogenous regressors." Journal of Applied Econometrics 30, 119–144.

Computation of global minimizer for partial structural change model

Description

'nldat()' computes the break dates of a partial structural change model for a pre-specified number of breaks 'm'. The procedure iterates between estimating the invariant and changing coefficients of 'x' and 'z' regressors until convergence, by noting that the residuals from linear regression model between 'y' and 'x' regressors is a pure structural change model, while the residuals from pure structural change model between 'y' and 'z' regressors is a linear regression

Usage

nldat(y, z, x, h, m, p, q, bigT, fixb, eps, maxi, betaini, printd)

Arguments

y

dependent variable in matrix form

z

matrix of regressors which coefficients are allowed to change across regimes

x

matrix of regressors which coefficients are constant across regime

h

minimum segment length

m

number of breaks

p

number of 'z' regressors

q

number of 'x' regressors

bigT

the sample size T

fixb

option to use initial \beta If 1, procedure requires betaini. If 0, procedure will not use initial beta values

eps

Convergence criterion (For partial change model ONLY)

maxi

Maximum number of iterations (For partial change model ONLY)

betaini

initial beta values. Required when use with option fixb

printd

option to print output from iterated estimations. If 1, the results for each iteration will be printed in console log. If 0, no output will be printed

Value

A list containing the following components:

glb

minimum global SSR

datevec

Vector of dates (optimal minimizers)

bigvec

Associated SSRs

References

Bai J, Perron P (1998). "Estimating and Testing Linear Models with Multiple Structural Changes" Econometrica, 66, 47-78. Bai J, Perron P (2003). "Computation and Analysis of Multiple Structural Change Models" Journal of Applied Econometrics 18, 1-22

SupF test for 0 vs i breaks

Description

Function compute the supF test statistics of testing procedure with null hypothesis: no break versus alternative hypothesis: i breaks.

Usage

pftest(y, z, i, q, bigT, datevec, prewhit, robust, x, p, hetdat, hetvar)

Arguments

y

dependent variables

z

independent variables with coefficients are allowed to change across regimes

i

number of breaks in the model

q

number of z regressors

bigT

sample period T

datevec

i estimated dates from the model

prewhit

Options for prewhitening process

robust, hetdat, hetvar

options for assumptions on error terms

x

independent variables with constant coefficients across regimes

p

number of x regressors

Value

ftest SupF test results

Construct diagonal matrix according to break date

Description

Function constructs a diagonal matrix of dimension (m+1) by (m+1) matrix with i-th entry \frac{T_{i} - T_{i-1}}{ T}

Usage

plambda(b, m, bigT)

Arguments

b

Estimated date of changes

m

Number of breaks

bigT

The sample size T

Value

lambda (m+1) by (m+1) diagonal matrix with i-th entry \frac{T_{i} - T_{i-1}}{ T}

Plot structural change model

Description

'plot_model()' visualizes any object of class 'model' with comparison between real, fitted values between model of 'm' breaks and null model of '0' breaks with options for confidence interval of break date.

Usage

plot_model(model, CI = 0.95, title = NULL)

Arguments

model

object of class 'model' in 'mbreaks' package

CI

confidence intervals for break date and coefficient estimates visualize in terms of fitted values

title

title of the graph

Value

No return value, called for plotting class 'model' object. For more details on 'model' class, see [compile_model]

Examples

rate = dofix('rate',data=real,fixn=2)
plot_model(rate,title='Ex-post US exchange rate')

Print information of 'mbreaks' comprehensive procedure

Description

'print' prints the class 'mdl' object with default showing only certain procedures called by 'mdl()' function including: 'seqtests' class object, 'sbtests' class object, and 'model' class object using KT information criterion

Usage

## S3 method for class 'mdl'
print(x, ...)

Arguments

x

class 'mdl' object

...

further arguments passed to or from other methods

Value

No return value, only for printing 'model', 'sbtests' and 'seqtests' class objects invoked during 'mdl()'.

Examples

rate = mdl('rate',data=real)
print(rate)

Summary output of a structural breaks 'model'

Description

'print' the output of the S3 class 'model' with all relevant information:

name of procedure used to obtain number of breaks in the model
print a table summarizing the break date estimation (including confidence interval for the estimated date)
print a table summarizing the estimated coefficients for 'z' regressors
print a table summarizing the estimated coefficients for 'x' regressors (if any)

Usage

## S3 method for class 'model'
print(x, ...)

Arguments

x

object of S3 class 'model'

...

further arguments passed to or from other methods.

Value

No return value, called for printing to console the following information in 'x':

Basic details of the model: name of prodecures invoked, number of estimated breaks, pure/partial structural change model,global min SSR
'date_tab' summarizes estimated break dates, see compile_model
'RS_tab' summarizes estimated coefficients allowed to change across regimes, see compile_model
'FS_tab' summarizes estimated coefficients constant across regimes, see compile_model

Print Sup F and UDMax tests

Description

'print' prints the following information from a 'sbtests' class object:

'supF1': A table reports sup F tests of 0 versus '1' upto 'm' breaks with critical values for 1%, 2.5%, 5%, and 10% significance levels.
'UDmax': A table reporting Double Max tests with critical values for 1%, 2.5%, 5%, and 10% significance levels.

Usage

## S3 method for class 'sbtests'
print(x, ...)

Arguments

x

class 'sbtests' object

...

further arguments passed to or from other methods

Value

No return value, only for printing formatted 'sbtests' class object to console

Examples

supF = dotest('inf','inflag',data=nkpc)
print(supF)

Print sequential SupF tests

Description

'print' prints the object of class 'seqtests' with the following information

Maximum number of breaks 'm' in the tests
'sfl' table with sequential sup F tests statistics of l versus l+1 breaks up to 'm' breaks

Usage

## S3 method for class 'seqtests'
print(x, ...)

Arguments

x

'seqtests' class object.

...

further arguments passed to or from other methods.

Value

No return value, only for printing formatted 'seqtests' class object to console

Examples

seq_supF = doseqtests('inf','inflag',data=nkpc)
print(seq_supF)

Construct diagonal matrix of estimated variance

Description

Function computes a diagonal matrix of dimension m+1 by m+1 with i-th entry is the estimated variance of residuals of segment i

Usage

psigmq(res, b, q, m, nt)

Arguments

res

big residual vector of the model

b

Estimated date of changes

q

Number of 'z' regressors

m

Number of breaks

nt

The size of 'z' regressors

Value

sigmat ('m'+1)x('m'+1) diagonal matrix with i-th entry equal to estimated variance of regime i

World Health Organization TB data

Description

Data set from the Garcia and Perron study's of ex-post exchange rate.

Usage

real

Format

## 'real' A data frame with 103 rows and 1 column:

rate: Real exchange rate

Source

Garcia, R. and Perron, P., 1996. "An analysis of the real interest rate under regime shifts." Review of Economics and Statistics 111–125.

SupF(l+1|l) test

Description

'spflp1' computes the test statistics of supF(l+1|l) test with null hypothesis is l='nseg-1' and alternative hypothesis is l+1. The l breaks under the null hypothesis are taken from the global minimization.

Usage

spflp1(bigvec, dt, nseg, y, z, h, q, prewhit, robust, x, p, hetdat, hetvar)

Arguments

bigvec

associated SSR of estimated break date under H0

dt

vector of estimated date under H0

nseg

number of segment under H1

y

matrix of dependent variable

z

matrix of variables with coefficients are allowed to change across regimes

h

minimum segment length

q

number of 'z' regressors

prewhit, robust, hetdat, hetvar

options on residuals/errors. For more details, please refer to [mdl()]

x

matrix of variables with constant coefficients across regimes

p

number of 'x' regressors

Value

A list that contains the following:

maxf: Maximum value of test
newd: Additional date in alternative hypothesis