MMCLRTest {MSTest}

Maximized Monte Carlo Likelihood Ratio Test

Description

This function performs the Maximized Monte Carlo likelihood ratio test (MMC-LRT) proposed in Rodriguez-Rondon & Dufour (2022).

Usage

MMCLRTest(Y, p, k0, k1, control = list())

Arguments

Y

Series to be tested. Must be a (T x q) matrix.

p

Number of autoregressive lags. Must be greater than or equal to 0.

k0

Number of regimes under null hypothesis. Must be greater than or equal to 1.

k1

Number of regimes under alternative hypothesis. Must be greater than k0.

control

List with test procedure options including:

• N: Integer determining the number of Monte Carlo simulations. Default is set to 99 as in paper.

• burnin: Number of simulated observations to remove from beginning. Default is 100.

• converge_check: String of NULL determining if convergence of model(s) should be verified. Allowed inputs are: "null", "alt", "both", or NULL. If NULL (default) no model convergence is verified.

• workers: Integer determining the number of workers to use for parallel computing version of test. Note that parallel pool must already be open. Default is 0.

• type: String that determines the type of optimization algorithm used. Arguments allowed are: "pso", "GenSA", and "GA". Default is "pso".

• eps: Double determining the constant value that defines a consistent set for search. Default is 0.1.

• CI_union: Boolean determining if union of set determined by eps and confidence set should be used to define consistent set for search. Default is TRUE.

• lambda: Double determining penalty on nonlinear constraint. Default is 100.

• stationary_constraint: Boolean determining if only stationary solutions are considered (if TRUE) or not (if FALSE). Default is TRUE.

• phi_low: Vector with lower bound for autoregressive parameters when optimizing. Default is NULL.

• phi_upp: Vector with upper bound for autoregressive parameters when optimizing. Default is NULL.

• P_low: Value with lower bound for transition probabilities when optimizing. Default is 0.

• P_upp: Value with upper bound for transition probabilities when optimizing. Default is 1.

• variance_constraint: Double used to determine the lower bound for variance in parameter set for search. Value should be between 0 and 1 as it is multiplied by consistent point estimates of variances. Default is 0.01 (i.e., 1% of consistent point estimates.

• silence: Boolean determining if optimization steps should be silenced (if TRUE) or not (if FALSE). Default is FALSE.

• threshold_stop: Double determining the global optimum of function. Default is 1.

• mdl_h0_control: List with restricted model options. See Nmdl, ARmdl, VARmdl, HMmdl, MSARmdl, or MSVARmdl documentation for available and default values.

• mdl_h1_control: List with unrestricted model options. See HMmdl, MSARmdl, or MSVARmdl documentation for available and default values.

• use_diff_init_sim: Value which determines the number of initial values to use when estimating models for null distribution. Default is set to use the same as specified in mdl_h0_control and mdl_h1_control.

• type_control: List with optimization algorithm options. See psoptim, GenSA, ga. Default is to set list(maxit = 200) so that maximum number of iterations is 200.

Value

List of class LMCLRTest (S3 object) with attributes including:

• mdl_h0: List with restricted model attributes. See Nmdl, ARmdl, VARmdl, HMmdl, MSARmdl, or MSVARmdl documentation for return values.

• mdl_h0: List with unrestricted model attributes. See HMmdl, MSARmdl, or MSVARmdl documentation for return values.

• LRT_0: Value of test statistic from observed data.

• LRN: A (N x 1) vector of test statistics from data simulated under the null hypothesis.

• pval: P-value of Local Monte Carlo Likelihood Ratio Test.

• LRN_cv: Vector with 90%, 95%, and 99% Monte Carlo critical values (from vector LRN).

• control: List with test procedure options used.

References

Rodriguez-Rondon, Gabriel and Jean-Marie Dufour. 2022. "Simulation-Based Inference for Markov Switching Models” JSM Proceedings, Business and Economic Statistics Section: American Statistical Association.

Rodriguez-Rondon, Gabriel and Jean-Marie Dufour. 2023. “Monte Carlo Likelihood Ratio Tests for Markov Switching Models.” Unpublished manuscript.

Examples

set.seed(1234)
# Define DGP of MS AR process
mdl_ms2 <- list(n     = 200, 
                mu    = c(5,10),
                sigma = c(1,4),
                phi   = c(0.5),
                k     = 2,
                P     = rbind(c(0.90, 0.10),
                              c(0.10, 0.90)))

# Simulate process using simuMSAR() function
y_ms_simu <- simuMSAR(mdl_ms2)


# Set test procedure options
mmc_control = list(N = 19,
                   burnin = 100,
                   converge_check = NULL,
                   eps = 0.1,
                   CI_union = TRUE,
                   silence = FALSE,
                   threshold_stop = 0.05 + 1e-6,
                   type = "pso",
                   maxit = 100,
                   mdl_h0_control = list(const  = TRUE, 
                                         getSE  = TRUE),
                   mdl_h1_control = list(msmu   = TRUE, 
                                         msvar  = TRUE,
                                         getSE  = TRUE,
                                         method = "EM",
                                         maxit  = 300,
                                         use_diff_init = 1))

  MMCtest <- MMCLRTest(y_ms_simu$y, p = 1 , k0 = 1 , k1 = 2, mmc_control)
  summary(MMCtest)