| Title: | Tests for a Structural Change in Multivariate Time Series |
|---|---|
| Description: | Flexible implementation of a structural change point detection algorithm for multivariate time series. It authorizes inclusion of trends, exogenous variables, and break test on the intercept or on the full vector autoregression system. Bai, Lumsdaine, and Stock (1998) <doi:10.1111/1467-937X.00051>. |
| Authors: | Loic Marechal [cre, aut] |
| Maintainer: | Loic Marechal <[email protected]> |
| License: | GPL |
| Version: | 0.1.0 |
| Built: | 2025-02-14 04:56:58 UTC |
| Source: | https://github.com/loicym/multibreaker |
Compute the AIC and BIC criteria for lags from 1 to q.max
AicBic(mat.y, q.max, mat.x = NULL, trend = FALSE, intercept = TRUE)AicBic(mat.y, q.max, mat.x = NULL, trend = FALSE, intercept = TRUE)
mat.y |
A matrix object of time series |
q.max |
The maximum lag considered |
mat.x |
An optional matrix of covariates |
trend |
If a trend is considered (default to false) |
intercept |
If the test is on the intercept (default to true) |
A data frame object that contains all AIC (first row) and BIC (second row) for all the q.max lags tested.
data(example_data) aic.bic <- AicBic(mat.y = example_data, q.max = 2, trend = FALSE, intercept = TRUE)data(example_data) aic.bic <- AicBic(mat.y = example_data, q.max = 2, trend = FALSE, intercept = TRUE)
#Compute the matrix of parameters and the covariance matrix of errors in OLS, FGLS, or IGLS mode.
Beta(mat.z, mat.y.ex, n.eq, p, est.mode, iter)Beta(mat.z, mat.y.ex, n.eq, p, est.mode, iter)
mat.z |
A matrix object of time series, regressor matrix |
mat.y.ex |
A matrix object of time series, regressor matrix |
n.eq |
number of equations in the VAR |
p |
number of observations |
est.mode |
estimation mode: "OLS", "FGLS", or "IGLS" |
iter |
If "IGLS" is used, how many iterations before stopping |
A list with the matrix of beta parameters as first element and the covariance matrix of error as second element.
Compute the confidence interval in time unit.
ConfidenceInterval(mat.g, mat.s, mat.sigma, mat.r, mat.beta, cv, p)ConfidenceInterval(mat.g, mat.s, mat.sigma, mat.r, mat.beta, cv, p)
mat.g |
A matrix object of time series |
mat.s |
A selection matrix |
mat.sigma |
The covariance matrix |
mat.r |
The selection vector of parameters |
mat.beta |
The matrix of parameters |
cv |
A vector of critical values |
p |
The length of the vector |
The difference in time unit around the break
Compute the list of matrices with correct dimensions to pass later in the computation
ConformableMatrix(mat.y, q, mat.x = NULL, trend = FALSE, intercept = TRUE)ConformableMatrix(mat.y, q, mat.x = NULL, trend = FALSE, intercept = TRUE)
mat.y |
The matrix object of time series |
q |
The chosen lag |
mat.x |
The matrix of optional covariates |
trend |
Whether we add a trend. Default = FALSE |
intercept |
Whether the break test is on the intercept only. Default = TRUE |
A list of conformed matrices
data(example_data) conf.matrix <- ConformableMatrix(mat.y = example_data, q = 2)data(example_data) conf.matrix <- ConformableMatrix(mat.y = example_data, q = 2)
Data generated with the function Simul() of the multibreakeR package with 100 time series observations (n = 100), five time series (p = 5), a break intensity of 1 (intensity = 1), and a break occuring at 35% of the sample (when.break = 0.35). These are also the default arguments of the Simul() function.
data(example_data)data(example_data)
A matrix object
https://github.com/loicym/multibreakeR
MultibreakeR generated data
list.breaks <- Main(mat.y = Simul(p = 2, when.break = 0.5), mat.x = NULL, trend = FALSE, intercept = TRUE, ci = c(0.9, 0.95, 0.99), est.mode = "OLS", iter = 3, aic.bic.mode = "AIC", q.max = 2, trim = 0.4, pos.break = FALSE)list.breaks <- Main(mat.y = Simul(p = 2, when.break = 0.5), mat.x = NULL, trend = FALSE, intercept = TRUE, ci = c(0.9, 0.95, 0.99), est.mode = "OLS", iter = 3, aic.bic.mode = "AIC", q.max = 2, trim = 0.4, pos.break = FALSE)
Compute the f-statistic for the break test
Fstat(mat.r, mat.beta, mat.z, p, mat.sigma)Fstat(mat.r, mat.beta, mat.z, p, mat.sigma)
mat.r |
The selection matrix for the parameters |
mat.beta |
The matrix of parameters |
mat.z |
The matrix of original and "breaking" time series |
p |
The number of observations |
mat.sigma |
The covariance matrix |
The f-statistic scalar
Compute the lags for the mat.y time series matrix
Lags(mat.y, q)Lags(mat.y, q)
mat.y |
The matrix of time series |
q |
The lag chosen |
A list of original (dependent) and lagged (independent) time series matrix
data(example_data) list.lags <- Lags(mat.y = example_data, q = 2)data(example_data) list.lags <- Lags(mat.y = example_data, q = 2)
Entry point for the whole computation of the algorithm of Bai, Lumsdaine, and Stock (1998)
Main( mat.y, mat.x = NULL, trend = FALSE, intercept = TRUE, ci = c(0.9, 0.95, 0.99), est.mode = "OLS", iter = 3, aic.bic.mode = "AIC", q.max = 2, trim = 0.15, pos.break = FALSE )Main( mat.y, mat.x = NULL, trend = FALSE, intercept = TRUE, ci = c(0.9, 0.95, 0.99), est.mode = "OLS", iter = 3, aic.bic.mode = "AIC", q.max = 2, trim = 0.15, pos.break = FALSE )
mat.y |
The matrix object of time series |
mat.x |
The matrix of optional covariates |
trend |
Whether we add a trend. Default = FALSE |
intercept |
Whether the break test is on the intercept only. Default = TRUE |
ci |
A vector of confidence intervals. Default = c(0.9, 0.95, 0.99) |
est.mode |
Estimation mode. Can be "OLS", "FGLS", or "IGLS" |
iter |
Maximum number of iterations in the "IGLS" mode. Default to 3 |
aic.bic.mode |
Can be "AIC" or "BIC" depending on the criterion chosen for the lag selection |
q.max |
Maximum lag tested for the AIC or BIC criterion |
trim |
Percentage for the trim value for the starting and ending window over which the algorithm is not tested. Default to 15% |
pos.break |
Whether we want to select the maximum positive break only and discard the negative ones. Default to FALSE |
A list of the vector of f-statistics, the maximum f-statistic retained, the confidence interval, the critical values, the break date, the original matrix of time series tested, the matrix with breaking and not breaking covariates, the index of the break in the time series, the size of the break (mean.shift), the optimal "AIC" or "BIC", a ggplot object (g1), and the trimmed dates.
data(example_data) list.results <- Main(mat.y = example_data, q = 2)data(example_data) list.results <- Main(mat.y = example_data, q = 2)
Generate a ggplot2 object to depict the break and the time series tested
PlotStats(my.dates, my.vars, f.stat, mat.ci = mat.ci, mat.y)PlotStats(my.dates, my.vars, f.stat, mat.ci = mat.ci, mat.y)
my.dates |
A vector of dates |
my.vars |
The variables tested |
f.stat |
The f-statistics |
mat.ci |
The matrix of confidence intervals |
mat.y |
The original time series |
A ggplot2 object
#compute the covariance matrix of errors as in Bai, Lumsdaine, and Stock (1998)
Sigma(mat.z, mat.y.ex, mat.beta, n.eq)Sigma(mat.z, mat.y.ex, mat.beta, n.eq)
mat.z |
A matrix of breaking and non breaking time series |
mat.y.ex |
A vectorized matrix of time series |
mat.beta |
The matrix of parameters |
n.eq |
The number of equations in the VAR system |
The covariance matrix of errors
#Simulate data to test the functions
Simul(n = 100, p = 5, intensity = 1, when.break = 0.5)Simul(n = 100, p = 5, intensity = 1, when.break = 0.5)
n |
The number of time series observations |
p |
The number of time series |
intensity |
The intensity of the break |
when.break |
When should the break be simulated (as a percentage of the time series sample) |
A matrix of time series with a common break
data(example_data) simul.data <- Simul(n = 100, p = 5, intensity = 1, when.break = 0.5)data(example_data) simul.data <- Simul(n = 100, p = 5, intensity = 1, when.break = 0.5)
Computes the critical values for a vector of confidence intervals proposed (ci)
Vdistr(ci)Vdistr(ci)
ci |
A vector of confidence intervals |
A vector of critical values
vect.cv <- Vdistr(ci = c(0.9, 0.95, 0.99))vect.cv <- Vdistr(ci = c(0.9, 0.95, 0.99))