irf_bands: Parametric confidence bands for impulse response functions
In pvarife: Panel VAR Models with Interactive Fixed Effects

irf_bands

R Documentation

Parametric confidence bands for impulse response functions

Description

Constructs confidence bands for structural impulse responses by drawing from the joint asymptotic distribution of the estimator and the common component (Theorem 2.3 of Tugan 2021). This is a parametric simulation, not a residual bootstrap.

Usage

irf_bands(
  fit,
  n_periods,
  shock = 1L,
  diff_vars = integer(0),
  identification = c("short_run", "long_run"),
  n_draw = 500L,
  level = 0.95,
  seed = NULL
)

Arguments

`fit`	An object of class `"pvarife_result"`.
`n_periods`	Positive integer. Number of IRF horizons.
`shock`	Positive integer. Index of the structural shock (default 1).
`diff_vars`	Integer vector. Variables to cumulate (default none).
`identification`	Character. `"short_run"` (default) or `"long_run"`. Passed to `compute_irf` for each draw. The median IRF returned is implicitly bias-corrected regardless of this choice (draws are centred on `\hat\beta - \hat b`).
`n_draw`	Positive integer. Number of simulation draws (default 500).
`level`	Numeric in (0, 1). Confidence level (default 0.95).
`seed`	Optional integer seed for reproducibility.

Details

For each of the n_draw repetitions, the function:

Draws \beta^{(b)} \sim N(\hat\beta - \hat b, \hat V) where \hat b and \hat V are the estimated bias and variance from asymptotic_var.
Draws the common component \tilde C_{i,t,k} from a normal with mean \hat F_t \hat\lambda_i and standard deviation

\sqrt{\hat\Xi^*_{i,t,k} / I + \hat\Xi^{**}_{i,t,k} / T},

capturing cross-sectional and time-series uncertainty in factor estimation.
Computes the IRF at (\beta^{(b)}, \tilde C^{(b)}).

The median and the (1-\mathrm{level})/2 and (1+\mathrm{level})/2 quantiles across draws give the point estimate and confidence bands.

Value

An object of class "pvarife_bands" with components:

irf: Point estimate (median across draws, bias-corrected), K \times n\_periods.
lower: Lower confidence bound, K \times n\_periods.
upper: Upper confidence bound, K \times n\_periods.
level: The confidence level used.
method: "asymptotic".

References

Tugan, M. (2021). Panel VAR models with interactive fixed effects. Econometrics Journal, 24, 225–246. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/ectj/utaa021")}

Examples

sim   <- sim_pvarife(n_units = 20, n_time = 15, n_vars = 2,
                     n_lags = 1, n_factors = 1, seed = 1)
fit   <- pvarife(sim$y, n_lags = 1, n_factors = 1, n_out = 5, n_in = 3)
bands <- irf_bands(fit, n_periods = 6, n_draw = 100, seed = 42)
plot(bands)

pvarife documentation built on June 11, 2026, 5:08 p.m.