Diebold-Mariano Test for Equal Predictive Accuracy

Tests whether two sets of forecast errors have equal predictive accuracy. Implements the modified test of Harvey, Leybourne, and Newbold (1997), which applies a finite-sample correction to the original Diebold and Mariano (1995) statistic and uses the t distribution rather than the normal. The Bartlett (triangular) kernel is used for HAC variance estimation, which guarantees a non-negative variance estimate.

Usage

nc_dm_test(
  e1,
  e2,
  alternative = c("two.sided", "less", "greater"),
  h = 1L,
  loss = c("squared", "absolute")
)

Arguments

e1

Numeric vector. Forecast errors from model 1.

e2

Numeric vector. Forecast errors from model 2 (same length).

alternative

Character. "two.sided", "less" (model 1 better), or "greater" (model 2 better).

h

Integer. Forecast horizon (default 1). Used for the Newey-West bandwidth and HLN correction.

loss

Character. Loss function: "squared" or "absolute".

Value

A list with components statistic, p_value, alternative, method, and n.

References

Diebold, F.X. and Mariano, R.S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263. doi:10.1080/07350015.1995.10524599

Harvey, D., Leybourne, S. and Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13(2), 281–291. doi:10.1016/S0169-2070(96)00719-4

Examples

# \donttest{
set.seed(1)
e1 <- rnorm(50, sd = 1)
e2 <- rnorm(50, sd = 1.5)
nc_dm_test(e1, e2)
#> $statistic
#> [1] -3.334762
#> 
#> $p_value
#> [1] 0.001633046
#> 
#> $alternative
#> [1] "two.sided"
#> 
#> $method
#> [1] "Diebold-Mariano (HLN)"
#> 
#> $n
#> [1] 50
#> 
# }