Max_lag source/target interpretation

[Daniele]

Hi all,

I'm computing the TE between two time series (mainly looking at the omnibus value) with a JidKraskovCMI estimator and a min lag sources=1. When I change the max_lag source (for both source and target) I see the TE decreasing monotonically with max_lag_source. I would expect it to increase, as I'm considering more and more time lags and eventually looking at the omnibus. Am I missing something?

Sincerely,
Daniele

------------------------- max_lag_source=max_lag_target=1 --  TE=0.352
Target: 1 - testing sources [0]

---------------------------- (1) include target candidates
candidate set: [(1, 1)]
testing candidate: (1, 1)
WARNING: Number of replications is not sufficient to generate the desired number of surrogates. Permuting samples in time instead.
maximum statistic, n_perm: 21

---------------------------- (2) include source candidates
candidate set current source: [(0, 1)]
testing candidate: (0, 1) maximum statistic, n_perm: 21

---------------------------- (3) prune candidates
selected vars sources [(0, 0)]
selected candidates current source: [(0, 1)]
 -- significant

---------------------------- (4) final statistics
selected variables: [(1, 1), (0, 1)]
omnibus test, n_perm: 21
 -- significant

sequential maximum statistic, n_perm: 21, testing 1 selected sources
final source samples: [(0, 1)]
final target samples: [(1, 1)]


te_bivar: {'sources_tested': [0], 'current_value': (1, 1), 'selected_vars_sources': [(0, 1)], 'selected_vars_target': [(1, 1)], 'selected_sources_pval': array([0.04761905]), 'selected_sources_te': array([0.35304261]), 'omnibus_te': 0.35302958587028377, 'omnibus_pval': 0.047619047619047616, 'omnibus_sign': True, 'te': array([0.35280597])}





-------------------------- max_lag_source=max_lag_target=3 -- TE = 0.195
Target: 1 - testing sources [0]

---------------------------- (1) include target candidates
candidate set: [(1, 1), (1, 2), (1, 3)]
testing candidate: (1, 1)
WARNING: Number of replications is not sufficient to generate the desired number of surrogates. Permuting samples in time instead.
maximum statistic, n_perm: 21
testing candidate: (1, 3) maximum statistic, n_perm: 21
testing candidate: (1, 2) maximum statistic, n_perm: 21

---------------------------- (2) include source candidates
candidate set current source: [(0, 1), (0, 2), (0, 3)]
testing candidate: (0, 3) maximum statistic, n_perm: 21
testing candidate: (0, 1) maximum statistic, n_perm: 21
testing candidate: (0, 2) maximum statistic, n_perm: 21

---------------------------- (3) prune candidates
selected vars sources [(0, 0), (0, 2), (0, 1)]
selected candidates current source: [(0, 3), (0, 1), (0, 2)]
testing candidate: (0, 1) minimum statistic, n_perm: 21
 -- significant

---------------------------- (4) final statistics
selected variables: [(1, 1), (1, 3), (1, 2), (0, 3), (0, 1), (0, 2)]
omnibus test, n_perm: 21
 -- significant

sequential maximum statistic, n_perm: 21, testing 3 selected sources

Stopping sequential max stats at candidate with rank 0.
final source samples: []
final target samples: [(1, 1), (1, 3), (1, 2)]


te_bivar: {'sources_tested': [0], 'current_value': (1, 3), 'selected_vars_sources': [], 'selected_vars_target': [(1, 1), (1, 3), (1, 2)], 'selected_sources_pval': array([], dtype=float64), 'selected_sources_te': array([], dtype=float64), 'omnibus_te': 0.19551824834081977, 'omnibus_pval': 0.047619047619047616, 'omnibus_sign': True, 'te': array([], dtype=float64)}