DLMMCpval_fun_min function

Moment-based MMC test (negative) p-value

This functions is used by numerical optimization algorithms for find negative of maximum p-value given parameter vector theta.

DLMMCpval_fun_min(
  theta,
  y,
  x,
  params,
  sim_stats,
  pval_type,
  stationary_ind,
  lambda
)

Arguments

• theta: Value of nuisance parameters. Specifically, these are the consistent estimates of nuisance parameters as discussed in Dufour & Luger (2017) LMC procedure.
• y: series being tested.
• x: lagged values of series.
• params: A (2 x 4) matrix with parameters to combine test statistics. See approxDistDL.
• sim_stats: A (N x 1) vector with test statistics. The last element is the test statistic from observed data.
• pval_type: String determining the type of method used to combine p-values. If set to "min" the min method of combining p-values is used as in Fisher 1932 and Pearson 1933. If set to "prod" the product of p-values is used as in Tippett 1931 and Wilkinson 1951.
• stationary_ind: Boolean indicator determining if only stationary solutions should be considered if TRUE or any solution can be considered if FALSE. Default is TRUE.
• lambda: Numeric value for penalty on stationary constraint not being met. Default is 100.

Returns

Negative Maximized Monte Carlo p-value.

References

Dufour, J. M., & Luger, R. 2017. "Identification-robust moment-based tests for Markov switching in autoregressive models." Econometric Reviews, 36(6-9), 713-727.