dm.test {forecast}

Diebold-Mariano test for predictive accuracy

Description

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

Usage

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

Arguments

e1

Forecast errors from method 1.

e2

Forecast errors from method 2.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

h

The forecast horizon used in calculating e1 and e2.

power

The power used in the loss function. Usually 1 or 2.

varestimator

a character string specifying the long-run variance estimator. Options are "acf" (default) or "bartlett".

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. The long-run variance estimator can either the auto-correlation estimator varestimator = "acf", or the estimator based on Bartlett weights varestimator = "bartlett" which ensures a positive estimate. Both long-run variance estimators are proposed in Diebold and Mariano (1995).

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.

varestimator

a character string describing the long-run variance estimator.

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.

Author(s)

George Athanasopoulos and Kirill Kuroptev

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)
accuracy(f2)
dm.test(residuals(f1), residuals(f2), h = 1)

# 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)
f2.out <- Arima(WWWusage[81:100], model = f2)
accuracy(f1.out)
accuracy(f2.out)
dm.test(residuals(f1.out), residuals(f2.out), h = 1)