DLMCTest function

Monte Carlo moment-based test for Markov switching model

This function performs the Local Monte Carlo moment-based test for Markov switching autoregressive models proposed in Dufour & Luger (2017).

DLMCTest(Y, p, control = list())

Arguments

• Y: Series to be tested

• p: Number of autoregressive lags.

• control: List with test procedure options including:

  • N: Integer determining the number of Monte Carlo simulations. Default is set to 99 as in paper.
  • simdist_N: Integer determining the number of simulations for CDF distribution approximation. Default is set to 10000.
  • getSE: Boolean indicator. If TRUE, standard errors for restricted model are estimated. If FALSE no standard errors are estimated. Default is TRUE.

Returns

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

• mdl_h0: List with restricted model attributes. This will be of class ARmdl if p\>0 or Nmdl otherwise (S3 objects). See ARmdl or Nmdl.
• theta: Value of nuisance parameters. Specifically, these are the consistent estimates of nuisance parameters as discussed in Dufour & Luger (2017) LMC procedure.
• S0: A (1 x 4)) matrix containing the four moment-based test statistics defined in (11) - (14) in Dufour & Luger (2017).
• F0_min: Test statistic value for min version of Local Monte Carlo moment-based test.
• F0_prod: Test statistic value for prod version of Local Monte Carlo moment-based test.
• FN_min: A (N x 1) vector with simulated test statistics for min version of Local Monte Carlo moment-based test under null hypothesis.
• FN_prod: A (N x 1) vector with simulated test statistics for prod version of Local Monte Carlo moment-based test under null hypothesis.
• pval_min: P-value for min version of Local Monte Carlo moment-based test.
• pval_prod: P-value for prod version of Local Monte Carlo moment-based test.
• FN_min_cv: Vector with 90%, 95%, and 99% Monte Carlo critical values for min version of Local Monte Carlo moment-based test.
• FN_prod_cv: Vector with 90%, 95%, and 99% Monte Carlo critical values for prod version of Local Monte Carlo moment-based test.
• control: List with test procedure options used.

Examples

set.seed(1234)
# load data used in Hamilton 1989 and extended data used in CHP 2014 
y84 <- as.matrix(hamilton84GNP$GNP_gr)
y10 <- as.matrix(chp10GNP$GNP_gr)

# Set test procedure options
lmc_control = list(N = 99,
                   simdist_N = 10000,
                   getSE = TRUE)

# perform test on Hamilton 1989 data
lmc_gnp84 <- DLMCTest(y84, p = 4, control = lmc_control)
summary(lmc_gnp84)

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.