Coveragelongmemory: Calculate the coverage of several long-memory models

Description

Generates coverage metrics for a parameter of interest using a specified long-memory model.

Usage

Coveragelongmemory(
  n,
  R,
  N,
  S,
  mu = 0,
  dist,
  method,
  B = NULL,
  nr.cores = 1,
  seed = 123,
  alpha,
  beta,
  start,
  sign = 0.05
)

Value

A data frame containing the following columns:

n: Size of each simulated series.
method: Statistical method used for simulation.
coverage: Proportion of true parameter values within the intervals.
avg_width: Average width of the intervals.
sd_width: Standard deviation of the interval widths.

Arguments

n: (type: numeric) size of the simulated series.
R: (type: numeric) number of realizations of the Monte Carlo experiments.
N: (type: numeric) sample size of each block.
S: (type: numeric) shifting places from block to block. Observe that the number of blocks M is determined by the following formula $M=\left\lfloor \frac{T-N}{S} + 1 \right\rfloor$, where $\left\lfloor . \right\rfloor$ takes a single numeric argument x and returns a numeric vector containing the integers formed by truncating the values in x toward 0.
mu: (type: numeric) trend coefficient of the regression model.
dist: (type: character) white noise distribution for calculating coverage, it includes the "normal", "exponential" and "uniform" univariate distributions.
method: (type: character) methods are asymptotic ("asym"), bootstrap percentile ("boot") and bootstrap-t ("boott").
B: (type: numeric) the number of bootstrap replicates, NULL indicates the asymptotic method.
nr.cores: (type: numeric) number of CPU cores to be used for parallel processing. 1 by default.
seed: (type: numeric) random number generator seed to generate the bootstrap samples.
alpha: (type: numeric) numeric vector with values to simulate the time varying autoregressive parameters of model LSAR(1), $\phi(u)$.
beta: (type: numeric) numeric vector with values to simulate the time varying scale factor parameters of model LSAR(1), $\sigma(u)$.
start: (type: numeric) numeric vector, initial values for parameters to run the model.
sign: nominal significance level

Details

This function estimates the parameters in the linear regression model for $t = 1, ..., T$, $$Y_{t,T} = X_{t,T} \beta + \epsilon_{t,T},$$ where a locally stationary fractional noise process (LSFN) is described by the equation: $$\epsilon_{t,T} = \sum_{j=0}^\infty \psi_j(u) \eta_{t-j}$$ for u=t/T in [0,1], where $\psi_j(u) = \frac{\Gamma[j + d(u)]}{\Gamma[j+1] \Gamma[d(u)]}$ and $d(u)$ is the smoothly varying long-memory coefficient. This model is referred to as locally stationary fractional noise (LSFN).

In this particular case, $d(u)$ is modeled as a linear polynomial, and $\sigma(u)$ as a quadratic polynomial.

Resampling methods evaluated:

asym: Asymptotic method that uses the asymptotic variance of the estimator, based on the Central Limit Theorem, to construct confidence intervals under the assumption of normality in large samples.
boot: Standard bootstrap that generates replicas of the estimator $\hat{\beta}$ by resampling the adjusted residuals $\hat{\epsilon}_t$. It approximates the distribution of the estimator by the variability observed in the bootstrap replicas of $\hat{\beta}$.
boott: Adjusted bootstrap that scales the bootstrap replicas of the estimator $\hat{\beta}$ by its standard error, aiming to refine the precision of the confidence interval and adjust for the variability in the parameter estimation.

For more details, see references.

References

Ferreira G., Mateu J., Vilar J.A., Muñoz J. (2020). Bootstrapping regression models with locally stationary disturbances. TEST, 30, 341-363.

Examples

Run this code

Coveragelongmemory(n=500,R=5,N=60,S=40,mu=0.5,dist="normal",method="asym",
beta=c(0.1,-2),alpha=c(0.15,0.25, 0.1),start = c(0.1,-2,0.15,0.2, 0.1))

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