liang_causality (pyleoclim.utils.causality.liang_causality)
- pyleoclim.utils.causality.liang_causality(y1, y2, npt=1, signif_test='isospec', nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995])[source]
Estimate the Liang information transfer from series y2 to series y1 with significance estimates using either an AR(1) test with series with the same persistence or surrogates with randomized phases.
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
npt (int >=1) – time advance in performing Euler forward differencing, e.g., 1, 2. Unless the series are generated with a highly chaotic deterministic system, npt=1 should be used
signif_test ({'isopersist', 'isospec'}) – the method for significance test see signif_isospec and signif_isopersist for details.
nsim (int) – the number of AR(1) surrogates for significance test
qs (list) – the quantiles for significance test
- Returns
res –
- A dictionary of results including:
- T21float
information flow from y2 to y1 (Note: not y1 -> y2!)
- tau21float
the standardized information flow from y2 to y1
- Zfloat
the total information flow from y2 to y1
- T21_noise_qslist
the quantiles of the information flow from noise2 to noise1 for significance testing
- tau21_noise_qslist
the quantiles of the standardized information flow from noise2 to noise1 for significance testing
- Return type
dict
See also
pyleoclim.utils.causality.granger_causality
information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist
significance test with AR(1) with same persistence
pyleoclim.utils.causality.causality.signif_isospec
significance test with surrogates with randomized phases
References
- Liang, X.S. (2013) The Liang-Kleeman Information Flow: Theory and
Applications. Entropy, 15, 327-360, doi:10.3390/e15010327
- Liang, X.S. (2014) Unraveling the cause-efect relation between timeseries.
Physical review, E 90, 052150
- Liang, X.S. (2015) Normalizing the causality between time series.
Physical review, E 92, 022126
- Liang, X.S. (2016) Information flow and causality as rigorous notions ab initio.
Physical review, E 94, 052201