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Test the non-Gaussianity of VARMA-LiNGAM residuals

Source: R/lingam_varma_diagnostics.r
test_varmalingam_residual_normality.Rd

LiNGAM assumes the error terms are non-Gaussian, so rejecting normality (small p-value) supports the model assumption. By default the test is run on the LiNGAM innovations e_t = (I - B0) n_t (the independent errors the model assumes), where n_t are the stored VARMA residuals; set on = "varma" to test the reduced-form VARMA residuals n_t directly instead.

Usage

test_varmalingam_residual_normality(
  result,
  method = "shapiro",
  alpha = 0.05,
  on = c("innovations", "varma")
)

Arguments

result

a VARMALiNGAMResult from lingam_varma()

method

normality test ("shapiro", "ks", "ad", "lillie", "jb"); see test_residual_normality() for package requirements

alpha

significance level (default 0.05)

on

which series to test: "innovations" (default, e_t = (I - B0) n_t) or "varma" (the reduced-form VARMA residuals n_t)

Value

a lingam_normality_test data frame (one row per variable), printed via print.lingam_normality_test().

References

Residual non-Gaussianity diagnostics inspired by the VARLiNGAM R code (Gauss_Tests) of Moneta, A., Entner, D., Hoyer, P. O., & Coad, A. (2013), Oxford Bulletin of Economics and Statistics, 75(5), 705-730. https://sites.google.com/site/dorisentner/publications/VARLiNGAM

Examples

s <- generate_varmalingam_sample(n = 1000, seed = 42)
m <- lingam_varma(s$data,
  order = c(1, 1), criterion = NULL,
  reg_method = "ols", prune = FALSE
)
test_varmalingam_residual_normality(m)
#> === Residual Normality Test ===
#> Method:         shapiro
#> Sample size:    999
#> Significance:   0.050
#> Non-Gaussian:   3 / 3 variables
#> 
#>  variable statistic   p_value is_non_gauss skewness kurtosis
#>        x0    0.9494 < 2.2e-16         TRUE    0.088   -1.222
#>        x1    0.9552 < 2.2e-16         TRUE    0.005   -1.230
#>        x2    0.9547 < 2.2e-16         TRUE   -0.042   -1.207
#> 
#> Interpretation:
#>   is_non_gauss = TRUE  -> rejects normality (supports LiNGAM assumption)
#>   is_non_gauss = FALSE -> cannot reject normality (LiNGAM may not fit)
#> 
#> All residuals are non-Gaussian. LiNGAM assumption is supported.