NEWS

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rbfmvar 2.1.0 (2026-09-28)

• The estimator now implements the RBFM-VAR correction of Chang (2000, equations 10 to 13). Previous versions used the OLS residuals in place of the process v_t of equation (11), computed the long-run covariance of the residuals instead of the cross covariance with v_t, and spread the row means of a correction matrix over all nonstationary regressors, so the reported "FM+" coefficients were not the RBFM-VAR estimates. The correction is now (Y'Z, Y+'W + T Delta+)(X'X)^{-1} with Y+' = Y' - Omega_ev Omega_vv^{-1} V', Delta+ = Omega_ev Omega_vv^{-1} Delta_vDw, v_t = (D2 y_{t-1}, D y_{t-1} - N D y_{t-2}) and Dw_t = (D2 y_{t-1}, D y_{t-1}). A test reproduces the formula directly. With the data generating process of Chang (2000, Section 5), the OLS biases match Table 1 of the paper and the RBFM-VAR biases have the same signs and orders of magnitude; the paper does not state the kernel or bandwidth it used, so exact replication is not possible.
• The estimation sample now starts at t = max(p + 1, 4) (the levels VAR(p) needs y_{t-p} and v_t needs D y_{t-2}).
• New internal estimate_cross_lrv(); estimate_onesided_lrv() sums k(j/K) T^{-1} sum_t a_{t+j} b_t' as in the convention of Chang (2000, p. 909); the Quadratic Spectral kernel now uses all lags (its weights do not vanish beyond the bandwidth). The automatic bandwidth is Andrews (1991) applied to v_t.
• granger_test(): the modified Wald statistic ignored the covariances between the tested coefficients (it summed squared t ratios). It now uses Sigma_e[i, i] (X'X)^{-1} for the tested block (Chang, 2000, eq. 20); the chi-square p-value is conservative (Theorem 2).
• irf(): the responses used only Pi_1 as a VAR(1) matrix, and the "bootstrap" intervals added random noise to the point estimates. The responses are now those of the levels VAR implied by the estimates, and the intervals come from a recursive-design residual bootstrap that re-estimates the model. fevd() inherits the correction.
• forecast(): forecasts were Pi_1 times the last fitted second difference. They are now level forecasts from the implied levels VAR, with the forecast error variance sum Psi_i Sigma_e Psi_i'.
• ic_table() returned nothing; it now reports the criteria from the stored data. Lag selection compares all lag orders on a common sample and counts n p parameters per equation (there is no constant).
• The fitted object now also contains data, XtX_inv and N_hat.

rbfmvar 2.0.3

• Corrected the DOI of Chang (2000), Econometric Theory 16(6), to 10.1017/S0266466600166058 (all occurrences). No changes to code.

rbfmvar 2.0.0

Initial Release

• Implements Residual-Based Fully Modified VAR (RBFM-VAR) estimator following Chang (2000).

• Core estimation:

  • rbfmvar(): Main estimation function for RBFM-VAR models.
  • Handles unknown mixtures of I(0), I(1), and I(2) variables.
  • FM+ bias correction for asymptotically valid inference.

• Lag selection:

  • Automatic lag selection via AIC, BIC, or HQ information criteria.
  • ic_table(): Display information criteria comparison.

• Long-run variance estimation:

  • Bartlett (Newey-West), Parzen, and Quadratic Spectral kernels.
  • Andrews (1991) automatic bandwidth selection.

• Inference:

  • granger_test(): Granger non-causality testing with modified Wald statistics.
  • granger_matrix(): Pairwise Granger causality tests.
  • Asymptotically chi-squared inference regardless of integration orders.

• Impulse response analysis:

  • irf(): Orthogonalized impulse response functions.
  • Bootstrap confidence intervals via Kilian (1998) method.

• Forecast error variance decomposition:

  • fevd(): Cholesky-identified variance decomposition.

• Forecasting:

  • forecast(): Out-of-sample forecasting with prediction intervals.

• Methods:

  • print(), summary(), plot() methods for all major objects.
  • coef(), residuals(), fitted(), vcov() extractors.

References

Chang, Y. (2000). Vector Autoregressions with Unknown Mixtures of I(0), I(1), and I(2) Components. Econometric Theory, 16(6), 905-926. doi:10.1017/S0266466600166058