Recursive identification of SVAR models via Cholesky decomposition
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 ε_t.
Matrix B corresponds to the decomposition of the least squares covariance matrix Σ_u=BΛ_t B'.
id.chol(x, order_k = NULL)
x |
An object of class 'vars', 'vec2var', 'nlVar'. Estimated VAR object |
order_k |
Vector. Vector of characters or integers specifying the assumed structure of the recursive causality. Change the causal ordering in the instantaneous effects without permuting variables and re-estimating the VAR model. |
A list of class "svars" with elements
B |
Estimated structural impact matrix B, i.e. unique decomposition of the covariance matrix of reduced form residuals |
n |
Number of observations |
method |
Method applied for identification |
order_k |
Ordering of the variables as assumed for recursive causality |
A_hat |
Estimated VAR parameter |
type |
Type of the VAR model, e.g. 'const' |
y |
Data matrix |
p |
Number of lags |
K |
Dimension of the VAR |
VAR |
Estimated input VAR object |
Luetkepohl, H., 2005. New introduction to multiple time series analysis, Springer-Verlag, Berlin.
# 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')Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.