qardl_simulate: Monte Carlo Simulation for QARDL

Description

Performs Monte Carlo simulation to assess the finite-sample properties of QARDL estimators under specified data generating processes.

Usage

qardl_simulate(
  nobs = 200L,
  reps = 1000L,
  tau = c(0.25, 0.5, 0.75),
  p = 1L,
  q = 1L,
  k = 1L,
  beta_true = NULL,
  phi_true = NULL,
  gamma_true = NULL,
  sigma_u = 1,
  sigma_x = 1,
  seed = NULL,
  parallel = FALSE,
  ncores = NULL
)

Value

An object of class "qardl_mc" containing:

beta_sim: Array of simulated beta estimates (k x ntau x reps)
phi_sim: Array of simulated phi estimates (p x ntau x reps)
gamma_sim: Array of simulated gamma estimates (k x ntau x reps)
beta_true: True beta values
phi_true: True phi values
gamma_true: True gamma values
bias_beta: Bias in beta estimates
rmse_beta: RMSE of beta estimates
coverage_beta: Empirical coverage of 95% CI for beta
reps: Number of replications
nobs: Sample size
tau: Vector of quantiles

Arguments

nobs: Integer. Sample size for each simulation. Default is 200.
reps: Integer. Number of Monte Carlo replications. Default is 1000.
tau: Numeric vector of quantiles. Default is c(0.25, 0.50, 0.75).
p: Integer. AR lag order. Default is 1.
q: Integer. Distributed lag order. Default is 1.
k: Integer. Number of covariates. Default is 1.
beta_true: Numeric vector. True long-run parameters (length k). Default is rep(1, k).
phi_true: Numeric vector. True AR parameters (length p). Default is rep(0.5, p).
gamma_true: Numeric vector. True impact parameters (length k). Default is rep(0.3, k).
sigma_u: Numeric. Standard deviation of the error term. Default is 1.
sigma_x: Numeric. Standard deviation of covariate innovations. Default is 1.
seed: Integer. Random seed for reproducibility. Default is NULL.
parallel: Logical. Use parallel processing. Default is FALSE.
ncores: Integer. Number of cores for parallel processing. Default is parallel::detectCores() - 1.

Details

The data generating process is: $$y_t = \sum_{i=1}^{p} \phi_i y_{t-i} + \sum_{j=1}^{k} \gamma_j x_{jt} + u_t$$

where $u_t \sim N(0, \sigma_u^2)$ and $x_{jt}$ follows a random walk with innovations $\sim N(0, \sigma_x^2)$.

References

Cho, J.S., Kim, T.-H., & Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188(1), 281-300. tools:::Rd_expr_doi("10.1016/j.jeconom.2015.01.003")

Examples

Run this code

# Small simulation for illustration
mc <- qardl_simulate(nobs = 100, reps = 50, tau = c(0.25, 0.50, 0.75),
                     p = 1, q = 1, k = 1, seed = 123)
print(mc)

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