rbfmvar: Residual-Based Fully Modified VAR Estimation

In rbfmvar: Residual-Based Fully Modified Vector Autoregression

Residual-Based Fully Modified VAR Estimation

Description

Estimates a Residual-Based Fully Modified Vector Autoregression (RBFM-VAR) model following Chang (2000). The RBFM-VAR procedure extends Phillips (1995) FM-VAR to handle any unknown mixture of I(0), I(1), and I(2) components without prior knowledge of the number or location of unit roots.

Usage

rbfmvar(
  data,
  lags = 2,
  max_lags = 8,
  ic = "none",
  kernel = "bartlett",
  bandwidth = -1,
  level = 95
)

Arguments

data	A numeric matrix or data frame containing the time series variables. Must have at least 2 columns.
lags	Integer. The VAR lag order p. Must be at least 1. Default is 2.
max_lags	Integer. Maximum number of lags to consider for information criterion selection. Default is 8.
ic	Character string specifying the information criterion for lag selection: "aic", "bic", "hq", or "none" (use lags directly). Default is "none".
kernel	Character string specifying the kernel for long-run variance estimation: "bartlett", "parzen", or "qs" (Quadratic Spectral). Default is "bartlett".
bandwidth	Numeric. Bandwidth for kernel estimation. If -1 (default), automatic bandwidth selection via Andrews (1991) is used.
level	Numeric. Confidence level for coefficient intervals (0-100). Default is 95.

Details

The RBFM-VAR model is specified as:

\Delta^2 y_t = \sum_{j=1}^{p-2} \Gamma_j \Delta^2 y_{t-j} + \Pi_1 \Delta y_{t-1} + \Pi_2 y_{t-1} + e_t

where \Delta is the difference operator and \Delta^2 = \Delta \circ \Delta.

The FM+ correction eliminates the second-order asymptotic bias that arises from the correlation between the regression errors and the innovations in integrated regressors. The estimator achieves:

• Zero mean mixed normal limiting distribution

• Chi-square Wald statistics for hypothesis testing

• Robustness to unknown integration orders

Value

An object of class "rbfmvar" containing:

F_ols

OLS coefficient matrix.

F_plus

FM+ corrected coefficient matrix.

SE_mat

Standard errors for FM+ coefficients.

Pi1_ols, Pi1_plus

Coefficient matrices for \Delta y_{t-1}.

Pi2_ols, Pi2_plus

Coefficient matrices for y_{t-1}.

Gamma_ols, Gamma_plus

Coefficient matrices for \Delta^2 y_{t-j} (if p >= 3).

Sigma_e

Residual covariance matrix.

Omega_ev, Omega_vv

Long-run variance components.

Delta_vdw

One-sided long-run covariance for FM correction.

residuals

Matrix of residuals from FM+ estimation.

fitted

Matrix of fitted values.

nobs

Number of observations in original data.

T_eff

Effective sample size after differencing.

n_vars

Number of variables.

p_lags

VAR lag order used.

bandwidth

Bandwidth used for LRV estimation.

kernel

Kernel used for LRV estimation.

ic

Information criterion used (if any).

varnames

Variable names.

call

The matched call.

References

Chang, Y. (2000). Vector Autoregressions with Unknown Mixtures of I(0), I(1), and I(2) Components. Econometric Theory, 16(6), 905-926. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1017/S0266466600166071")}

Phillips, P. C. B. (1995). Fully Modified Least Squares and Vector Autoregression. Econometrica, 63(5), 1023-1078. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2171721")}

Andrews, D. W. K. (1991). Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59(3), 817-858. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2938229")}

Examples

# Simulate a simple VAR(2) process
set.seed(123)
n <- 200
e <- matrix(rnorm(n * 3), n, 3)
y <- matrix(0, n, 3)
for (t in 3:n) {
  y[t, ] <- 0.3 * y[t-1, ] + 0.2 * y[t-2, ] + e[t, ]
}
colnames(y) <- c("y1", "y2", "y3")

# Estimate RBFM-VAR
fit <- rbfmvar(y, lags = 2)
summary(fit)

# With automatic lag selection
fit_aic <- rbfmvar(y, max_lags = 6, ic = "aic")
summary(fit_aic)

rbfmvar documentation built on April 9, 2026, 9:08 a.m.