id.cvm {svars}

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

x

An object of class 'vars', 'vec2var', 'nlVar'. Estimated VAR object

dd

Object of class 'indepTestDist' (generated by 'indepTest' from package 'copula'). A simulated independent sample of the same size as the data. If not supplied, it will be calculated by the function

itermax

Integer. IMaximum number of iterations for DEoptim

steptol

Numeric. Tolerance for steps without improvement for DEoptim

iter2

Integer. Number of iterations for the second optimization

Value

A list of class "svars" with elements

B

Estimated structural impact matrix B, i.e. unique decomposition of the covariance matrix of reduced form errors

A_hat

Estimated VAR parameter

method

Method applied for identification

n

Number of observations

type

Type of the VAR model, e.g. 'const'

y

Data matrix

p

Number of lags

K

Dimension of the VAR

rotation_angles

Rotation angles, which lead to maximum independence

inc

Indicator. 1 = second optimization increased the estimation precision. 0 = second optimization did not increase the estimation precision

test.stats

Computed test statistics of independence test

iter1

Number of iterations of first optimization

test1

Minimum test statistic from first optimization

test2

Minimum test statistic from second optimization

VAR

Estimated input VAR object

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')