bcVAR {bcVAR} | R Documentation |
Estimation of the bias-corrected least squares of a VAR(p) model.
bcVAR(data = data, p = 1, type = c("const", "none"), ...)
data |
Data item containing the endogenous variables with the dimension T \times K, where T is the length of the time series and K is the number of endogenous variables. |
p |
Integer for the lag order (default is p = 1). |
type |
Type of deterministic regressors to include. |
... |
Currently not used. |
Estimates a VAR by OLS and applies the bias correction proposed by Pope (1990). The model is of the following form:
Y_t = \bold{v} + \bold{A}Y_{t-1} + \bold{u}_t,
where Y_t is a Kp \times 1 vector of endogenous
variables and \bold{u}_t with the same dimension is assumed to be iid white noise. The companion matrix \bold{A} is of dimension Kp \times Kp. The intercept vector \bold{v} is of dimension Kp \times 1. By setting the type argument to const
, the intercept vector \bold{v} is included. The bias of the least squares (LS) estimator \hat{\bold{A}} for \bold{A} is
-B_{\bold{A}}/T + O(T^{-3/2}),
where
B_{\bold{A}} = Σ_U≤ft[(I_{Kp}-\bold{A}')^{-1}+\bold{A}'(I_{Kp}-\bold{A}'^2)^{-1}+∑_{λ} λ(I_{Kp}-λ \bold{A}')^{-1}\right] Γ_Y(0)^{-1},
Γ_Y(0)^{-1} = E(Y_tY_t'), Σ_U = E(U_tU_t') and the sum over the eigenvalues λ of \bold{A} weighted by their multiplicities. Adding B_{\hat{\bold{A}}}/T to \hat{\bold{A}} yields the bias-corrected LS estimator \hat{\bold{A}}^{BC}. For more details regarding the bias-corrected LS see for example chapter 2 of Kilian, L., & Lütkepohl, H. (2017). The resulting object of bcVAR()
has the same class attribute as the object of VAR()
from the ‘vars’ package of Pfaff, B. (2008).
A list with class attribute ‘varest
’ (class attribute of the ‘vars’ package) holding the
following elements:
varresult |
List of pseudo ‘ |
datamat |
The data matrix of the endogenous and explanatory variables. |
y |
The data matrix of the endogenous variables. |
p |
An integer specifying the lag order. |
K |
An integer specifying the dimension of the VAR. |
obs |
An integer specifying the number of used observations. |
totobs |
An integer specifying the total number of observations. |
restrictions |
Always |
call |
The |
Simon Röck
Pope, A. L. (1990). “Biases of Estimators in Multivariate Non-Gausssian Autoregressions”, Journal of Time Series Analysis, 11(3), 249–258. doi: 10.1111/j.1467-9892.1990.tb00056.x
Kilian, L., & Lütkepohl, H. (2017). Structural Vector Autoregressive Analysis, Cambridge University Press, Cambridge.
Pfaff, B. (2008). “VAR, SVAR and SVEC Models: Implementation within R Package vars”, Journal of Statistical Software, 27(4), 1–32. doi: 10.18637/jss.v027.i04
## load data of package data("USmacro", package = "bcVAR") ## detrend data (substract mean) dataDT <- apply(USmacro, 2, function(y) y - mean(y)) ## bias-corrected LS VAR(4) model (see Chapter 2 of Kilian, L., & Luetkepohl, H. (2017)) bcVAR(dataDT, p = 4, type = "const")