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).

1. MSE : d = (e1)^2 - (e2)^2
2. MAD : d = abs(e1) - abs(e2)
3. MAPE: d = abs((e1 - actual)/(actual))
4. Poly: d = (e1)^power - (e2)^power

The null hypothesis is E[d] = 0.

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 rt

Output:

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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