The Diebold-Mariano test compares the forecast accuracy of two forecast methods.

dm.test(e1, e2, alternative = c("two.sided", "less", "greater"), h = 1,
power = 2)

## Arguments

e1 Forecast errors from method 1. Forecast errors from method 2. a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. The forecast horizon used in calculating e1 and e2. The power used in the loss function. Usually 1 or 2.

## Value

A list with class "htest" containing the following components:

statistic

the value of the DM-statistic.

parameter

the forecast horizon and loss function power used in the test.

alternative

a character string describing the alternative hypothesis.

p.value

the p-value for the test.

method

a character string with the value "Diebold-Mariano Test".

data.name

a character vector giving the names of the two error series.

## Details

This function implements the modified test proposed by Harvey, Leybourne and Newbold (1997). The null hypothesis is that the two methods have the same forecast accuracy. For alternative="less", the alternative hypothesis is that method 2 is less accurate than method 1. For alternative="greater", the alternative hypothesis is that method 2 is more accurate than method 1. For alternative="two.sided", the alternative hypothesis is that method 1 and method 2 have different levels of accuracy.

## References

Diebold, F.X. and Mariano, R.S. (1995) Comparing predictive accuracy. Journal of Business and Economic Statistics, 13, 253-263.

Harvey, D., Leybourne, S., & Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of forecasting, 13(2), 281-291.

## Examples


# Test on in-sample one-step forecasts
f1 <- ets(WWWusage)
f2 <- auto.arima(WWWusage)
accuracy(f1)#>                     ME    RMSE      MAE       MPE     MAPE      MASE      ACF1
#> Training set 0.2243266 3.40781 2.761668 0.2629465 2.162415 0.6102792 0.2308014accuracy(f2)#>                     ME     RMSE      MAE       MPE     MAPE      MASE
#> Training set 0.3035616 3.113754 2.405275 0.2805566 1.917463 0.5315228
#>                     ACF1
#> Training set -0.01715517dm.test(residuals(f1),residuals(f2),h=1)#>
#> 	Diebold-Mariano Test
#>
#> data:  residuals(f1)residuals(f2)
#> DM = 1.9078, Forecast horizon = 1, Loss function power = 2, p-value =
#> 0.05932
#> alternative hypothesis: two.sided
#>
# Test on out-of-sample one-step forecasts
f1 <- ets(WWWusage[1:80])
f2 <- auto.arima(WWWusage[1:80])
f1.out <- ets(WWWusage[81:100],model=f1)#> Model is being refit with current smoothing parameters but initial states are being re-estimated.
#> Set 'use.initial.values=TRUE' if you want to re-use existing initial values.f2.out <- Arima(WWWusage[81:100],model=f2)
accuracy(f1.out)#>                     ME    RMSE      MAE       MPE     MAPE      MASE      ACF1
#> Training set 0.2100836 3.24835 2.570459 0.1203497 1.352355 0.4246845 0.2287215accuracy(f2.out)#>                    ME     RMSE      MAE       MPE     MAPE      MASE
#> Training set 1.081679 3.329012 2.437119 0.6810673 1.375924 0.4026544
#>                      ACF1
#> Training set -0.004460367dm.test(residuals(f1.out),residuals(f2.out),h=1)#>
#> 	Diebold-Mariano Test
#>
#> data:  residuals(f1.out)residuals(f2.out)
#> DM = -0.14392, Forecast horizon = 1, Loss function power = 2, p-value =
#> 0.8871
#> alternative hypothesis: two.sided
#>