Financial Econometrics

HARMONIA.

Discovery of multivariate relationships among three or more assets: cointegrating spaces, sparse baskets, and mean-reverting portfolios that can be defended statistically, temporally, and economically.

Flagship — HARMONIA

Multi-Asset Cointegration & Mean-Reverting Basket Engineering

The object is X_t = (A_1, …, A_N) and z_t = w'X_t — relationships that may not be visible pair-by-pair, turned into small, interpretable baskets. Not pairs; not Granger–Lee strict multicointegration.

What HARMONIA provides

Six technical phases — from pair to N-asset, and from a cointegrating space to a tradable basket.

Phase 1 — SYSTEM Pair → N-asset foundations.

Phase 2 — DISCOVERY Space → basket — cointegration rank and a cointegrating space, not a unique basket.

Phase 3 — PORTFOLIO Constraints + direct mean-reverting portfolios.

Phase 4 — ECONOMICS Speed vs amplitude — holding time, cost, and capital.

Phase 5 — DYNAMICS Stability + tracking — regularisation, turnover, and dynamic basket tracking.

Phase 6 — SCIENCE Search + lab + OOS — combinatorial search, multiple testing, and the discovery laboratory.