Tests the null hypothesis that two forecasting methods have equal predictive ability (UEPA), with an optional small-sample correction by Harvey, Leybourne, and Newbold (1997).
Arguments
- e1
Numeric vector of forecast errors from model 1 (benchmark).
- e2
Numeric vector of forecast errors from model 2 (competitor).
- h
Integer; forecast horizon. Default
1.- loss
Character; loss function to use.
"SE"for squared error (default),"AE"for absolute error.- alternative
Character; alternative hypothesis.
"two.sided"(default),"less"(model 2 is better), or"greater"(model 1 is better).- correction
Logical; apply the Harvey, Leybourne, and Newbold (1997) finite-sample correction? Default
TRUE.
Value
A list with class "dm_test" containing:
- statistic
The (possibly corrected) DM test statistic.
- pvalue
P-value.
- alternative
The alternative hypothesis used.
- correction
Whether HLN correction was applied.
- h
Forecast horizon.
- n
Number of observations.
- loss
Loss function used.
References
Diebold, F.X. and Mariano, R.S. (1995). Comparing Predictive Accuracy. Journal of Business & Economic Statistics, 13(3), 253-263.
Harvey, D., Leybourne, S., and Newbold, P. (1997). Testing the Equality of Prediction Mean Squared Errors. International Journal of Forecasting, 13(2), 281-291.
Examples
set.seed(42)
e1 <- rnorm(100)
e2 <- rnorm(100, mean = 0.1)
dm_test(e1, e2)
#>
#> ╭────────────────────────────────────────────────────╮
#> │ Modified Diebold-Mariano Test (HLN, 1997) │
#> ├────────────────────────────────────────────────────┤
#> │ H0: Equal predictive ability │
#> │ H1: Methods have different predictive ability │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Test Results: │
#> │ DM statistic: 1.5039 │
#> │ P-value: 0.1358 │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Details: │
#> │ Observations (n): 100 │
#> │ Forecast horizon (h): 1 │
#> │ Loss function: SE │
#> │ Reference distribution: t(99) │
#> ╰────────────────────────────────────────────────────╯
#>