bcVAR {bcVAR}R Documentation

Bias-Corrected Least Squares Estimator for VAR Models

Description

Estimation of the bias-corrected least squares of a VAR(p) model.

Usage

bcVAR(data = data, p = 1, type = c("const", "none"), ...)

Arguments

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.

Details

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).

Value

A list with class attribute ‘varest’ (class attribute of the ‘vars’ package) holding the following elements:

varresult

List of pseudo ‘lm’ objects with the bias-corrected LS of the VAR(p) process. Pseudo ‘lm’ objects, because the objects are not generated by lm().

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 NULL. Zero restrictions of the VAR(p) are not implemented.

call

The call to bcVAR().

Author(s)

Simon Röck

References

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

See Also

VAR

Examples

## 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")

[Package bcVAR version 0.1-0 Index]