Partial Information Decomposition for Joint Trading Indicators

Summary

The article explains partial information decomposition (PID), which separates the information two indicators provide about a target into redundant, unique, and synergistic parts. It describes three alternative redundancy definitions—I_min, I_MMI, and I_ccs—and shows why their results can differ, including on logic gates such as XOR and COPY. The method discretizes market features and targets into equal-frequency bins, builds a joint count table, and estimates the information atoms from that table.

For significance, the article compares observed atoms with a permutation null, using block shuffling to preserve some time dependence. Its XAUUSD example scans indicator pairs against forward volatility and reports a candidate pair whose synergy exceeds the null percentile, while emphasizing finite-sample upward bias, block-length sensitivity, and the limited resolution of p-values with few permutations. The method depends on binning choices and the selected redundancy axiom; its market example is evidence of an observed association, not proof of predictive value or profitability.

Key ideas

• PID partitions joint information into redundancy, source-specific information, and synergy.
• The decomposition is underdetermined by mutual information alone, so the redundancy definition changes the resulting atoms.
• Equal-frequency discretization creates a joint count table from continuous market features and targets.
• Permutation nulls are needed because finite samples can make information atoms appear positive even for noise.
• Block length and the number of null draws affect the reliability and resolution of significance estimates.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.