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.

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 test statistics follow the student-T distribution with degree of freedom (T - 1).

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)

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.

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Copyright (c) 2017 John Tsang

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