The Granger Causality Test

Table of Contents

TLDR

The institutional forensics script's Granger causality module — which applies a statistical test that checks whether one type of event reliably happens before another — tests whether shell company formation dates systematically precede wire transfer activity. Across 53 tracked entities and 224 wire transfers, the pattern holds: companies are formed, accounts are opened, and money follows — sometimes within nine days (PAPER TRAIL Project, 2026).

The Question

If someone creates a shell company and then begins wiring millions of dollars through it three weeks later, is the sequence coincidental? Do it once and it might be. Do it across dozens of entities spanning five jurisdictions over a decade, and the question becomes statistical.

Granger causality is a statistical framework that tests whether one time series is useful in forecasting another. It does not prove causation in the philosophical sense. It tests whether lagged values of one variable improve prediction of another beyond what the second variable's own history provides. In this context: do entity formation dates improve prediction of when wire transfers will occur, beyond what wire transfer timing alone predicts? (Granger, 1969; PAPER TRAIL Project, 2026).

The Data

The test draws from two sources. Entity formation dates come from verified corporate registry records — New York Department of State, Delaware Division of Corporations, USVI corporate filings — corroborated during external verification against public databases. Wire transfer dates come from the 224 parsed transactions in the corpus, totaling $24.1 million, with 58.9% dated after recovery efforts using a Vision Language Model (VLM, an AI system that reads text from images of documents) (PAPER TRAIL Project, 2026).

The institutional forensics script exports the results to two files: the time series used in the test, and the temporal overlap window for each entity-wire pair (PAPER TRAIL Project, 2026).

The Pattern

The formation-to-activity intervals tell the story.

Southern Financial LLC was registered in the USVI on March 26, 2013. Its Deutsche Bank brokerage account opened August 19, 2013 — 146 days later. Southern Financial went on to process $606.9 million in inflows, making it the highest-volume financial entity in the network by an order of magnitude (PAPER TRAIL Project, 2026).

The Butterfly Trust was formed in 2013. Its Deutsche Bank accounts opened January 24, 2014. Over the relationship's lifetime, the Trust disbursed $2.65 million through 120-plus wire transfers to beneficiaries including three designated co-conspirators (NYDFS, 2020; PAPER TRAIL Project, 2026).

JEGE Inc. was incorporated in Delaware on September 7, 2000. JEGE LLC was formed in the USVI on October 19, 2012 — twelve years later, mirroring the broader corporate migration from mainland jurisdictions to the tax-advantaged USVI. This is not a formation-to-wire interval. It is a formation-to-formation interval, with the second entity inheriting the operational role of the first (PAPER TRAIL Project, 2026).

The shortest interval in the corpus belongs to Birch Tree Br LLC. It was incorporated in Florida on August 14, 2018. Its TD Bank account opened August 23, 2018 — nine days later. The entity existed for barely more than a week before it began receiving financial flows (PAPER TRAIL Project, 2026).

The Deutsche Bank to TD Bank Migration

The February through May 2019 migration from Deutsche Bank to TD Bank provides a natural experiment for the Granger test. Deutsche Bank terminated the Epstein relationship by letter on December 21, 2018 (NYDFS, 2020). In the months that followed, new TD Bank accounts were opened and immediately began receiving wire transfers from the closing Deutsche Bank accounts. Multiple wire memos reference "to close DB account" as the stated purpose (PAPER TRAIL Project, 2026).

HBRK Associates opened its TD Bank account on April 18, 2019. Harlequin Dane's TD account dated to April 29, 2015 — earlier than the migration, but it became a primary conduit during the Deutsche Bank exit. Birch Tree Br's Florida incorporation and near-immediate TD account opening in August 2018 preceded the formal termination letter by four months, suggesting the migration was anticipated before Deutsche Bank sent its notice (PAPER TRAIL Project, 2026).

The Granger test captures this: entity formation and account opening events cluster temporally before bursts of wire transfer activity, not after.

The Null Hypothesis

The null hypothesis is straightforward: shell company creation and wire transfer timing are independent events. Entities are formed for routine business purposes on their own schedule. Wire transfers occur according to their own operational logic. The two time series are unrelated.

The alternative hypothesis is that entity formation is preparatory — that shell companies are created specifically to serve as conduits for subsequent financial flows, and that the temporal ordering is not coincidental but functional.

The Granger test does not prove the alternative hypothesis. It tests whether the data is more consistent with the alternative than with the null. When Birch Tree Br LLC is incorporated and its bank account opens nine days later, the null hypothesis requires us to believe this is coincidence. When the same pattern repeats across JEGE, Southern Financial, the Butterfly Trust, and the Deutsche Bank-to-TD Bank migration entities, the null hypothesis becomes increasingly difficult to sustain (PAPER TRAIL Project, 2026).

What the Test Cannot Do

Granger causality has a well-known limitation: it identifies temporal precedence, not mechanism. It cannot tell you why someone formed an entity before wiring money through it. It can only tell you that the formation came first, consistently, across the corpus (Granger, 1969).

The causal mechanism — the intent behind the sequence — lives in documents the test does not read: board resolutions, formation memos, attorney-client communications. Some of those documents are in the corpus. Many are in the 42% that remains unreleased. The Granger test points to where the questions should be asked. The answers require a different kind of investigation.

References

Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.

New York Department of Financial Services. (2020). Consent order under New York Banking Law: Deutsche Bank AG [Regulatory order]. https://www.dfs.ny.gov/reports_and_publications/press_releases/pr202007061

PAPER TRAIL Project. (2026). Institutional forensics granger_causality module [Script]. app/scripts/18_institutional_analysis.py.

PAPER TRAIL Project. (2026). Granger time series export [Data]. _exports/institutional/granger_time_series.csv.

PAPER TRAIL Project. (2026). Entity formation wire overlap export [Data]. _exports/institutional/entity_formation_wire_overlap.csv.

PAPER TRAIL Project. (2026). Corporate registry verification [Data]. research/CORROBORATION_REPORT.md.

PAPER TRAIL Project. (2026). TD Bank SAR account opening dates [Data]. research/td_bank_sar_extraction.md.

PAPER TRAIL Project. (2026). Institutional forensics methodology [Data]. research/INSTITUTIONAL_FORENSICS.md.