BootLRTest {MSTest}

Bootstrap Likelihood Ratio Test

Description

This function performs the bootstrap likelihood ratio test discussed in Qu & Zhuo (2021) and Kasahara & Shimotsu (2018).

Usage

BootLRTest(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:

• B: Integer determining the number of bootstrap simulations. Default is set to 999.

• 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.

• 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.

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

Qu, Zhongjun, and Fan Zhuo. 2021. “Likelihood Ratio-Based Tests for Markov Regime Switching.” The Review of Economic Studies 88 (2): 937–968.

Kasahara, Hiroyuk, and Katsum Shimotsu. 2018. “Testing the number of regimes in Markov regime switching models.” arXiv preprint arXiv:1801.06862.

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 Unpublished manuscript.