# dm.test

##### Diebold-Mariano test for predictive accuracy

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
)
```

##### 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.

##### 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.

##### Value

A list with class `"htest"`

containing the following
components:

the value of the DM-statistic.

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

a character string describing the alternative hypothesis.

the p-value for the test.

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

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

##### 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

```
# NOT RUN {
# 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)
# }
```

*Documentation reproduced from package forecast, version 8.12, License: GPL-3*