Interaction between monetary policy and the stock market

Description

A five dimensional time series model which is commonly used to analyze the interaction between monetary policy and the stock market.
Monthly observations from 1970M1 to 2007M6:

All series, with exception of the commodity price index (c), are taken from the FRED database and transformed as in Luetkepohl & Netsunajev (2017). The commodity price index comes from the World Bank. A more detailed description of the data and a corresponding VAR model implementation can be found in Luetkepohl & Netsunajev (2017).

Usage

LN

Format

A data.frame containing 450 observations on 5 variables.

Source

Luetkepohl H., Netsunajev A., 2017. "Structural vector autoregressions with smooth transition in variances."
Journal of Economic Dynamics and Control, 84, 43 - 57. ISSN 0165-1889.

US macroeconomic time series

Description

The time series of output gap (x), inflation (pi) and interest rate (r) are taken from the FRED database and transformed as in Herwartz & Ploedt (2016). The trivariate time series model is commonly used to analyze monetary policy shocks.
Quarterly observations from 1965Q1 to 2008Q3:

A more detailed description of the data and a corresponding VAR model implementation can be found in Herwartz & Ploedt (2016).

Usage

USA

Format

A data.frame containing 174 observations on 3 variables.

Source

Herwartz, H. & Ploedt, M., 2016. Simulation Evidence on Theory-based and Statistical Identification under Volatility Breaks, Oxford Bulletin of Economics and Statistics, 78, 94-112.
Data originally from FRED database of the Federal Reserve Bank of St. Louis.

Bootstrap after Bootstrap

Description

Bootstrap intervals based on bias-adjusted estimators

Usage

ba.boot(x, nc = 1)

Arguments

Value

A list of class "sboot" with elements

References

Kilian, L. (1998). Small-sample confidence intervals for impulse response functions. Review of Economics and Statistics 80, 218-230.

See Also

mb.boot, wild.boot

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
summary(x1)

# Bootstrap
bb <- mb.boot(x1, b.length = 15, nboot = 300, n.ahead = 30, nc = 1, signrest = NULL)
summary(bb)
plot(bb, lowerq = 0.16, upperq = 0.84)

# Bias-adjusted bootstrap
bb2 <- ba.boot(bb, nc = 1)
plot(bb2, lowerq = 0.16, upperq = 0.84)

Counterfactuals for SVAR Models

Description

Calculation of Counterfactuals for an identified SVAR object 'svars' derived by function id.st( ), id.cvm( ),id.cv( ),id.dc( ) or id.ngml( ).

Usage

cf(x, series = 1, transition = 0)

Arguments

Value

A list with class attribute "hd" holding the Counterfactuals as data frame.

References

Kilian, L., Luetkepohl, H., 2017. Structural Vector Autoregressive Analysis, Cambridge University Press.

See Also

id.cvm, id.dc, id.ngml, id.cv, id.garch or id.st

Examples

v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
x2 <- cf(x1, series = 2)
plot(x2)

Chow Test for Structural Break

Description

The Chow test for structural change is implemented as sample-split and break-point test (see Luetkepohl and Kraetzig, 2004, p. 135). An estimated VAR model and the presupposed structural break need to be provided.

Usage

chow.test(
  x,
  SB,
  nboot = 500,
  start = NULL,
  end = NULL,
  frequency = NULL,
  format = NULL,
  dateVector = NULL
)

Arguments

Value

A list of class "chow" with elements

References

Luetkepohl, H., 2005. New introduction to multiple time series analysis, Springer-Verlag, Berlin.
Luetkepohl, H., Kraetzig, M., 2004. Applied time series econometrics, Cambridge University Press, Cambridge.

See Also

stability

Examples

# Testing for structural break in USA data
#' # data contains quartlery observations from 1965Q1 to 2008Q2
# assumed structural break in 1979Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
z1 <- chow.test(v1, SB = 59)
summary(z1)

#Using stability() to find potential break point and sample split
x1 <- stability(v1, type = "mv-chow-test")
plot(x1)
z1.1 <- chow.test(x1)
summary(z1.1)
#Or using sample split as benchmark
x1$break_point <- FALSE
z1.1 <- chow.test(x1)
summary(z1.1)

#Structural brake via Dates
#given that time series vector with dates is available
dateVector <- seq(as.Date("1965/1/1"), as.Date("2008/7/1"), "quarter")
z2 <- chow.test(v1, SB = "1979-07-01", format = "%Y-%m-%d", dateVector = dateVector)
summary(z2)

# alternatively pass sequence arguments directly
z3 <- chow.test(v1, SB = "1979-07-01", format = "%Y-%m-%d",
                start = "1965-01-01", end = "2008-07-01",
                frequency = "quarter")
summary(z3)

# or provide ts date format (For quarterly, monthly, weekly and daily frequencies only)
z4 <- chow.test(v1, SB = c(1979,3))
summary(z4)

Forecast error variance decomposition for SVAR Models

Description

Calculation of forecast error variance decomposition for an identified SVAR object 'svars' derived by function id.st( ), id.cvm( ),id.cv( ),id.dc( ) or id.ngml( ).

Usage

## S3 method for class 'svars'
fevd(x, n.ahead = 10, ...)

Arguments

Value

A list with class attribute "svarfevd" holding the forecast error variance decompositions as data frames.

References

Kilian, L., Luetkepohl, H., 2017. Structural Vector Autoregressive Analysis, Cambridge University Press.

See Also

id.cvm, id.garch, id.dc, id.ngml, id.cv or id.st

Examples

v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
x2 <- fevd(x1, n.ahead = 30)
plot(x2)

Historical decomposition for SVAR Models

Description

Calculation of historical decomposition for an identified SVAR object 'svars' derived by function id.st( ), id.cvm( ),id.cv( ),id.dc( ) or id.ngml( ).

Usage

hd(x, series = 1, transition = 0)

Arguments

Value

A list with class attribute "hd" holding the historical decomposition as data frame.

References

Kilian, L., Luetkepohl, H., 2017. Structural Vector Autoregressive Analysis, Cambridge University Press.

See Also

id.cvm, id.dc, id.ngml, id.cv, id.garch or id.st

Examples

v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
x2 <- hd(x1, series = 2)
plot(x2)

Recursive identification of SVAR models via Cholesky decomposition

Description

Given an estimated VAR model, this function uses the Cholesky decomposition to identify the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the decomposition of the least squares covariance matrix \Sigma_u=B\Lambda_t B'.

Usage

id.chol(x, order_k = NULL)

Arguments

Value

A list of class "svars" with elements

References

Luetkepohl, H., 2005. New introduction to multiple time series analysis, Springer-Verlag, Berlin.

See Also

For alternative identification approaches see id.st, id.cvm, id.cv, id.dc or id.ngml

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.chol(v1)
x2 <- id.chol(v1, order_k = c("pi", "x", "i")) ## order_k = c(2,1,3)
summary(x1)


# impulse response analysis
i1 <- irf(x1, n.ahead = 30)
i2 <- irf(x2, n.ahead = 30)
plot(i1, scales = 'free_y')
plot(i2, scales = 'free_y')

Identification of SVAR models based on Changes in volatility (CV)

Description

Given an estimated VAR model, this function applies changes in volatility to identify the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the decomposition of the pre-break covariance matrix \Sigma_1=B B'. The post-break covariance corresponds to \Sigma_2=B\Lambda B' where \Lambda is the estimated unconditional heteroskedasticity matrix.

Usage

id.cv(
  x,
  SB,
  SB2 = NULL,
  start = NULL,
  end = NULL,
  frequency = NULL,
  format = NULL,
  dateVector = NULL,
  max.iter = 50,
  crit = 0.001,
  restriction_matrix = NULL
)

Arguments

Value

A list of class "svars" with elements

References

Rigobon, R., 2003. Identification through Heteroskedasticity. The Review of Economics and Statistics, 85, 777-792.

Herwartz, H. & Ploedt, M., 2016. Simulation Evidence on Theory-based and Statistical Identification under Volatility Breaks. Oxford Bulletin of Economics and Statistics, 78, 94-112.

Luetkepohl, H. & Meitz, M. & Netsunajev, A. & and Saikkonen, P., 2021. Testing identification via heteroskedasticity in structural vector autoregressive models. Econometrics Journal, 24, 1-22.

See Also

For alternative identification approaches see id.st, id.garch, id.cvm, id.dc or id.ngml

Examples

#' # data contains quartlery observations from 1965Q1 to 2008Q2
# assumed structural break in 1979Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.cv(v1, SB = 59)
summary(x1)

# switching columns according to sign patter
x1$B <- x1$B[,c(3,2,1)]
x1$B[,3] <- x1$B[,3]*(-1)

# Impulse response analysis
i1 <- irf(x1, n.ahead = 30)
plot(i1, scales = 'free_y')

# Restrictions
# Assuming that the interest rate doesn't influence the output gap on impact
restMat <- matrix(rep(NA, 9), ncol = 3)
restMat[1,3] <- 0
x2 <- id.cv(v1, SB = 59, restriction_matrix = restMat)
summary(x2)

# In alternative Form
restMat <- diag(rep(1,9))
restMat[7,7]= 0
x2 <- id.cv(v1, SB = 59, restriction_matrix = restMat)
summary(x2)

#Structural brake via Dates
# given that time series vector with dates is available
dateVector = seq(as.Date("1965/1/1"), as.Date("2008/7/1"), "quarter")
x3 <- id.cv(v1, SB = "1979-07-01", format = "%Y-%m-%d", dateVector = dateVector)
summary(x3)

# or pass sequence arguments directly
x4 <- id.cv(v1, SB = "1979-07-01", format = "%Y-%m-%d", start = "1965-01-01", end = "2008-07-01",
frequency = "quarter")
summary(x4)

# or provide ts date format (For quarterly, monthly, weekly and daily frequencies only)
x5 <- id.cv(v1, SB = c(1979, 3))
summary(x5)

#-----# Example with three covariance regimes

x6 <- id.cv(v1, SB = 59, SB2 = 110)
summary(x6)

Independence-based identification of SVAR models via Cramer-von Mises (CVM) distance

Description

Given an estimated VAR model, this function applies independence-based identification for the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the unique decomposition of the least squares covariance matrix \Sigma_u=B B' if the vector of structural shocks \epsilon_t contains at most one Gaussian shock (Comon, 1994). A nonparametric dependence measure, the Cramer-von Mises distance (Genest and Remillard, 2004), determines least dependent structural shocks. The minimum is obtained by a two step optimization algorithm similar to the technique described in Herwartz and Ploedt (2016).

Usage

id.cvm(x, dd = NULL, itermax = 500, steptol = 100, iter2 = 75)

Arguments

Value

A list of class "svars" with elements

References

Herwartz, H., 2018. Hodges Lehmann detection of structural shocks - An Analysis of macroeconomic dynamics in the Euro Area, Oxford Bulletin of Economics and Statistics
Herwartz, H. & Ploedt, M., 2016. The macroeconomic effects of oil price shocks: Evidence from a statistical identification approach, Journal of International Money and Finance, 61, 30-44
Comon, P., 1994. Independent component analysis, A new concept?, Signal Processing, 36, 287-314
Genest, C. & Remillard, B., 2004. Tests of independence and randomness based on the empirical copula process, Test, 13, 335-370

See Also

For alternative identification approaches see id.st, id.garch, id.cv, id.dc or id.ngml

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
cob <- copula::indepTestSim(v1$obs, v1$K, verbose=FALSE)
x1 <- id.cvm(v1, dd = cob)
summary(x1)

# switching columns according to sign pattern
x1$B <- x1$B[,c(3,2,1)]
x1$B[,3] <- x1$B[,3]*(-1)

# impulse response analysis
i1 <- irf(x1, n.ahead = 30)
plot(i1, scales = 'free_y')

Independence-based identification of SVAR models build on distance covariances (DC) statistic

Description

Given an estimated VAR model, this function applies independence-based identification for the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the unique decomposition of the least squares covariance matrix \Sigma_u=B B' if the vector of structural shocks \epsilon_t contains at most one Gaussian shock (Comon, 1994). A nonparametric dependence measure, the distance covariance (Szekely et al, 2007), determines least dependent structural shocks. The algorithm described in Matteson and Tsay (2013) is applied to calculate the matrix B.

Usage

id.dc(x, PIT = FALSE)

Arguments

Value

A list of class "svars" with elements

References

Matteson, D. S. & Tsay, R. S., 2013. Independent Component Analysis via Distance Covariance, pre-print
Szekely, G. J.; Rizzo, M. L. & Bakirov, N. K., 2007. Measuring and testing dependence by correlation of distances Ann. Statist., 35, 2769-2794
Comon, P., 1994. Independent component analysis, A new concept?, Signal Processing, 36, 287-314

See Also

For alternative identification approaches see id.st, id.garch, id.cvm, id.cv or id.ngml

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
summary(x1)

# switching columns according to sign pattern
x1$B <- x1$B[,c(3,2,1)]
x1$B[,3] <- x1$B[,3]*(-1)

# impulse response analysis
i1 <- irf(x1, n.ahead = 30)
plot(i1, scales = 'free_y')

Identification of SVAR models through patterns of GARCH

Description

Given an estimated VAR model, this function uses GARCH-type variances to identify the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the decomposition of the least squares covariance matrix \Sigma_u=B\Lambda_t B', where \Lambda_t is the estimated conditional heteroskedasticity matrix.

Usage

id.garch(
  x,
  max.iter = 5,
  crit = 0.001,
  restriction_matrix = NULL,
  start_iter = 50
)

Arguments

Value

A list of class "svars" with elements

References

Normadin, M. & Phaneuf, L., 2004. Monetary Policy Shocks: Testing Identification Conditions under Time-Varying Conditional Volatility. Journal of Monetary Economics, 51(6), 1217-1243.

Lanne, M. & Saikkonen, P., 2007. A Multivariate Generalized Orthogonal Factor GARCH Model. Journal of Business & Economic Statistics, 25(1), 61-75.

Luetkepohl, H. & Milunovich, G. 2016. Testing for identification in SVAR-GARCH models. Journal of Economic Dynamics and Control, 73(C):241-258

See Also

For alternative identification approaches see id.st, id.cvm, id.cv, id.dc or id.ngml

Examples

# data contains quartlery observations from 1965Q1 to 2008Q2
# assumed structural break in 1979Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.garch(v1)
summary(x1)

# Impulse response analysis
i1 <- irf(x1, n.ahead = 30)
plot(i1, scales = 'free_y')

# Restrictions
# Assuming that the interest rate doesn't influence the output gap on impact
restMat <- matrix(rep(NA, 9), ncol = 3)
restMat[1,3] <- 0
x2 <- id.garch(v1, restriction_matrix = restMat)
summary(x2)

Non-Gaussian maximum likelihood (NGML) identification of SVAR models

Description

Given an estimated VAR model, this function applies identification by means of a non-Gaussian likelihood for the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the unique decomposition of the least squares covariance matrix \Sigma_u=B B' if the vector of structural shocks \epsilon_t contains at most one Gaussian shock (Comon, 94). A likelihood function of independent t-distributed structural shocks \epsilon_t=B^{-1}u_t is maximized with respect to the entries of B and the degrees of freedom of the t-distribution (Lanne et al., 2017).

Usage

id.ngml(x, stage3 = FALSE, restriction_matrix = NULL)

Arguments

Value

A list of class "svars" with elements

References

Lanne, M., Meitz, M., Saikkonen, P., 2017. Identification and estimation of non-Gaussian structural vector autoregressions. J. Econometrics 196 (2), 288-304.
Comon, P., 1994. Independent component analysis, A new concept?, Signal Processing, 36, 287-314

See Also

For alternative identification approaches see id.st, id.garch, id.cvm, id.dc or id.cv

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.ngml(v1)
summary(x1)

# switching columns according to sign pattern
x1$B <- x1$B[,c(3,2,1)]
x1$B[,3] <- x1$B[,3]*(-1)

# impulse response analysis
i1 <- irf(x1, n.ahead = 30)
plot(i1, scales = 'free_y')

Identification of SVAR models by means of a smooth transition (ST) in covariance

Description

Given an estimated VAR model, this function uses a smooth transition in the covariance to identify the structural impact matrix B of the corresponding SVAR model

y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.

Matrix B corresponds to the decomposition of the pre-break covariance matrix \Sigma_1=B B'. The post-break covariance corresponds to \Sigma_2=B\Lambda B' where \Lambda is the estimated heteroskedasticity matrix.

Usage

id.st(
  x,
  c_lower = 0.3,
  c_upper = 0.7,
  c_step = 5,
  c_fix = NULL,
  transition_variable = NULL,
  gamma_lower = -3,
  gamma_upper = 2,
  gamma_step = 0.5,
  gamma_fix = NULL,
  nc = 1,
  max.iter = 5,
  crit = 0.001,
  restriction_matrix = NULL,
  lr_test = FALSE
)

Arguments

Value

A list of class "svars" with elements

References

Luetkepohl H., Netsunajev A., 2017. Structural vector autoregressions with smooth transition
in variances. Journal of Economic Dynamics and Control, 84, 43 - 57. ISSN 0165-1889.

See Also

For alternative identification approaches see id.cv, id.garch, id.cvm, id.dc, or id.ngml

Examples

# data contains quartlery observations from 1965Q1 to 2008Q2
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.st(v1, c_fix = 80, gamma_fix = 0)
summary(x1)
plot(x1)

# switching columns according to sign patter
x1$B <- x1$B[,c(3,2,1)]
x1$B[,3] <- x1$B[,3]*(-1)

# Impulse response analysis
i1 <- irf(x1, n.ahead = 30)
plot(i1, scales = 'free_y')

# Example with same data set as in Luetkepohl and Nestunajev 2017
v1 <- vars::VAR(LN, p = 3, type = 'const')
x1 <- id.st(v1, c_fix = 167, gamma_fix = -2.77)
summary(x1)
plot(x1)

# Using a lagged endogenous transition variable
# In this example inflation with two lags
inf <- LN[-c(1, 449, 450), 2]*(1/sd(LN[-c(1, 449, 450), 2]))
x1_inf <- id.st(v1, c_fix = 4.41, gamma_fix = 0.49, transition_variable = inf)
summary(x1_inf)
plot(x1_inf)

Impulse Response Functions for SVAR Models

Description

Calculation of impulse response functions for an identified SVAR object 'svars' derived by function id.cvm( ),id.cv( ),id.dc( ), id.ngml( ) or id.st( ).

Usage

## S3 method for class 'svars'
irf(x, ..., n.ahead = 20)

Arguments

Value

A list with class attribute "svarirf" holding the impulse response functions as data frame.

References

Luetkepohl, H., 2005. New introduction to multiple time series analysis, Springer-Verlag, Berlin.

See Also

id.cvm, id.dc, id.ngml, id.cv or id.st

Examples

v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.ngml(v1)
x2 <- irf(x1, n.ahead = 20)
plot(x2)

Chi-square test for joint hypotheses

Description

Based on an existing bootstrap object, the test statistic allows to test joint hypotheses for selected entries of the structural matrix B. The test statistic reads as

(Rvec(\widehat{B}) - r)'R(\widehat{\mbox{Cov}}[vec(B^*)])^{-1}R'(Rvec(\widehat{b} - r)) \sim \chi^2_J,

where \widehat{\mbox{Cov}}[vec(B^*)] is the estimated covariance of vectorized bootstrap estimates of structural parameters. The composite null hypothesis is H_0: Rvec(B)= r.

Usage

js.test(x, R, r = NULL)

Arguments

Value

A list of class "jstest" with elements

References

Herwartz, H., 2018. Hodges Lehmann detection of structural shocks - An analysis of macroeconomic dynamics in the Euro Area, Oxford Bulletin of Economics and Statistics

See Also

mb.boot, wild.boot

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)

# Bootstrapping of SVAR
bb <- wild.boot(x1, nboot = 1000, n.ahead = 30)

# Testing the hypothesis of a lower triangular matrix as
# relation between structural and reduced form errors
R <- rbind(c(0,0,0,1,0,0,0,0,0), c(0,0,0,0,0,0,1,0,0),
           c(0,0,0,0,0,0,0,1,0))
c.test <- js.test(bb, R)
summary(c.test)

Moving block bootstrap for IRFs of identified SVARs

Description

Calculating confidence bands for impulse response via moving block bootstrap

Usage

mb.boot(
  x,
  design = "recursive",
  b.length = 15,
  n.ahead = 20,
  nboot = 500,
  nc = 1,
  dd = NULL,
  signrest = NULL,
  signcheck = TRUE,
  itermax = 300,
  steptol = 200,
  iter2 = 50
)

Arguments

Value

A list of class "sboot" with elements

References

Brueggemann, R., Jentsch, C., and Trenkler, C., 2016. Inference in VARs with conditional heteroskedasticity of unknown form. Journal of Econometrics 191, 69-85.
Herwartz, H., 2017. Hodges Lehmann detection of structural shocks - An analysis of macroeconomic dynamics in the Euro Area, Oxford Bulletin of Economics and Statistics.

See Also

id.cvm, id.dc, id.ngml, id.garch, id.cv or id.st

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
summary(x1)

# impulse response analysis with confidence bands
# Checking how often theory based impact relations appear
signrest <- list(demand = c(1,1,1), supply = c(-1,1,1), money = c(-1,-1,1))
bb <- mb.boot(x1, b.length = 15, nboot = 500, n.ahead = 30, nc = 1, signrest = signrest)
summary(bb)

# Plotting IRFs with confidance bands
plot(bb, lowerq = 0.16, upperq = 0.84)

# With different confidence levels
plot(bb, lowerq = c(0.05, 0.1, 0.16), upperq = c(0.95, 0.9, 0.84))

# Halls percentile
plot(bb, lowerq = 0.16, upperq = 0.84, percentile = 'hall')

# Bonferroni bands
plot(bb, lowerq = 0.16, upperq = 0.84, percentile = 'bonferroni')

Structural stability of a VAR(p)

Description

Computes an empirical fluctuation process according to a specified method from the generalized fluctuation test framework. The test utilises the function efp() and its methods from package ‘strucchange’. Additionally, the function provides the option to compute a multivariate chow test.

Usage

## S3 method for class 'varest'
stability(
  x,
  type = c("OLS-CUSUM", "Rec-CUSUM", "Rec-MOSUM", "OLS-MOSUM", "RE", "ME", "Score-CUSUM",
    "Score-MOSUM", "fluctuation", "mv-chow-test"),
  h = 0.15,
  dynamic = FALSE,
  rescale = TRUE,
  ...
)

Arguments

Details

For details, please refer to documentation efp and chow.test.

Value

A list with either class attribute ‘varstabil’ or ‘chowpretest’ holding the following elements in case of class ‘varstabil’:

In case of class ‘chowpretest’ the list consists of the following elements:

Author(s)

Bernhard Pfaff, Alexander Lange, Bernhard Dalheimer, Simone Maxand, Helmut Herwartz

References

Zeileis, A., F. Leisch, K. Hornik and C. Kleiber (2002), strucchange: An R Package for Testing for Structural Change in Linear Regression Models, Journal of Statistical Software, 7(2): 1-38, doi:10.18637/jss.v007.i02

and see the references provided in the reference section of efp and chow.test, too.

See Also

VAR, plot, efp, chow.test

Examples

data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
var.2c.stabil <- stability(var.2c, type = "OLS-CUSUM")
var.2c.stabil
plot(var.2c.stabil)

data(USA)
v1 <- VAR(USA, p = 6)
x1 <- stability(v1, type = "mv-chow-test")
plot(x1)

svars: Data-driven identification of structural VAR models

Description

This package implements data-driven identification methods for structural vector autoregressive (SVAR) models as described in Lange et al. (2021) doi:10.18637/jss.v097.i05. Based on an existing VAR model object, the structural impact matrix B may be obtained via different forms of heteroskedasticity or independent components.

Details

The main functions to retrieve structural impact matrices are:

• id.cv

  Identification via changes in volatility,

• id.cvm

  Independence-based identification of SVAR models based on Cramer-von Mises distance,

• id.dc

  Independence-based identification of SVAR models based on distance covariances,

• id.garch

  Identification through patterns of conditional heteroskedasticity,

• id.ngml

  Identification via Non-Gaussian maximum likelihood,

• id.st

  Identification by means of smooth transition in covariance.

All of these functions require an estimated var object. Currently the classes 'vars' and 'vec2var' from the vars package, 'nlVar', which includes both VAR and VECM, from the tsDyn package as well as the list from MTS package are supported. Besides these core functions, additional tools to calculate confidence bands for impulse response functions using bootstrap techniques as well as the Chow-Test for structural changes are implemented. The USA dataset is used to showcase the functionalities in examples throughout the package.

Author(s)

• Alexander Lange alexander.lange@uni-goettingen.de

• Bernhard Dalheimer bernhard.dalheimer@uni-goettingen.de

• Helmut Herwartz hherwartz@uni-goettingen.de

• Simone Maxand simone.maxand@helsinki.fi

Wild bootstrap for IRFs of identified SVARs

Description

Calculating confidence bands for impulse response functions via wild bootstrap techniques (Goncalves and Kilian, 2004).

Usage

wild.boot(
  x,
  design = "fixed",
  distr = "rademacher",
  n.ahead = 20,
  nboot = 500,
  nc = 1,
  dd = NULL,
  signrest = NULL,
  signcheck = TRUE,
  itermax = 300,
  steptol = 200,
  iter2 = 50,
  rademacher = "deprecated"
)

Arguments

Value

A list of class "sboot" with elements

References

Goncalves, S., Kilian, L., 2004. Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics 123, 89-120.
Herwartz, H., 2017. Hodges Lehmann detection of structural shocks - An analysis of macroeconomic dynamics in the Euro Area, Oxford Bulletin of Economics and Statistics

See Also

id.cvm, id.dc, id.garch, id.ngml, id.cv or id.st

Examples

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)
summary(x1)

# impulse response analysis with confidence bands
# Checking how often theory based impact relations appear
signrest <- list(demand = c(1,1,1), supply = c(-1,1,1), money = c(-1,-1,1))
bb <- wild.boot(x1, nboot = 500, n.ahead = 30, nc = 1, signrest = signrest)
summary(bb)

# Plotting IRFs with confidance bands
plot(bb, lowerq = 0.16, upperq = 0.84)

# With different confidence levels
plot(bb, lowerq = c(0.05, 0.1, 0.16), upperq = c(0.95, 0.9, 0.84))

# Halls percentile
plot(bb, lowerq = 0.16, upperq = 0.84, percentile = 'hall')

# Bonferroni bands
plot(bb, lowerq = 0.16, upperq = 0.84, percentile = 'bonferroni')