Diebold-Mariano Test
This Python function dm_test implements the Diebold-Mariano Test (1995) with modification suggested by Harvey et. al (1997) to statitsitcally identify forecast accuracy equivalance for 2 sets of predictions.
Description
Suppose that the difference between the first list of prediction and the actual values is e1 and the second list of prediction and the actual value is e2. The length of time-series is T.
Then d can be defined based on different criterion (crit).
- MSE : d = (e1)^2 - (e2)^2
- MAD : d = abs(e1) - abs(e2)
- MAPE: d = abs((e1 - actual)/(actual))
- Poly: d = (e1)^power - (e2)^power
The test statistics follow the student-T distribution with degree of freedom (T - 1).
File
| File Name | Description | |
|---|---|---|
| 1. | dm_test.py | This file contains the function to implement the DM test. |
Input
| Input Parameter | Description | |
|---|---|---|
| 1. | actual_lst | The list of actual values |
| 2. | pred1_lst | The first list of predicted values |
| 3. | pred2_lst | The second list of predicted values |
| 4. | h | The number of steps ahead of the prediction. The default value is 1. |
| 5. | crit | A string specifying the criterion. The default value is MSE. |
| 6. | power | The power for crit equal "poly". It is only meaningful when crit is "poly". The default value is 2. (i.e. E[d] = (e1)^2 - (e2)^2) |
Return
| Names of Return | Description | |
|---|---|---|
| 1. | DM | The DM test statistics |
| 2. | p-value | The p-value of DM test statistics |
Example
Sample Script:
from dm_test import dm_test
import random
random.seed(123)
actual_lst = range(0,100)
pred1_lst = range(0,100)
pred2_lst = range(0,100)
actual_lst = random.sample(actual_lst,100)
pred1_lst = random.sample(pred1_lst,100)
pred2_lst = random.sample(pred2_lst,100)
rt = dm_test(actual_lst,pred1_lst,pred2_lst,h = 1, crit="MAD")
print rt
rt = dm_test(actual_lst,pred1_lst,pred2_lst,h = 1, crit="MSE")
print rt
rt = dm_test(actual_lst,pred1_lst,pred2_lst,h = 1, crit="poly", power=4)
print rtOutput:
dm_return(DM=1.3275742446369585, p_value=0.18737195617455585)
dm_return(DM=1.2112523589452902, p_value=0.22868210381769466)
dm_return(DM=0.9124498079287283, p_value=0.36374861695187799)Reference
Harvey, D., Leybourne, S., & Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of forecasting, 13(2), 281-291.
Diebold, F. X. and Mariano, R. S. (1995), Comparing predictive accuracy, Journal of business & economic statistics 13(3), 253-264.
Licence
MIT License
Copyright (c) 2017 John Tsang
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