Coveragelongmemory {LSEbootLS}

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
)

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.

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.

References

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

Examples

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))