HARMONIA
Multi-Asset Cointegration & Mean-Reverting Basket Engineering
Multi-Asset Cointegration & Mean-Reverting Basket Engineering
$1,800
Mission and vision
Mission
Teach 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.
Vision
Researchers who extract small, interpretable baskets from a relationship space — not a pair spread, and not Granger–Lee strict multicointegration.
Why HARMONIA
HARMONIA is Multi-Asset Cointegration & Mean-Reverting Basket Engineering.
The wordmark is harmony among many parts: a cointegrating space turned into a small basket. It does not mean Granger–Lee strict multicointegration (I(2) accumulations of equilibrium errors). That distinction is a special module.
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 baskets. It is not the retired TAC stages (cointegration · failure · relations). It is not Forex-as-identity. It is not the two-asset pair path.
Who it is for
Quantitative researchers, systematic traders, statistical-arbitrage developers, and financial engineers who already command bivariate cointegration (ARGOS or equivalent). Linear algebra, time series, ADF, and spread construction are assumed.
What it is not
Not ARGOS (two-asset pairs). Not Granger–Lee. Not a five-name recipe. Lecture bodies are not authored yet.
What you'll be able to do
- Move from (A, B) → spread to z = w'X on three or more assets
- Estimate cointegration rank and a cointegrating space — not a unique basket
- Extract sparse, constrained, tradable vectors from that space
- Compare Econometric-First discovery with Objective-First (direct MRP)
- Validate generating procedures under stability, costs, multiplicity, and causal OOS
Course content
Phase 1 — SYSTEM
Module 1 — From Pair to Multi-Asset System
Module 2 — Johansen & VECM
Module 3 — Cointegrating Spaces
Phase 2 — DISCOVERY
Module 1 — From Cointegrating Space to Tradable Basket
Module 2 — Sparse Cointegration
Module 3 — High-Dimensional Relationship Selection
Phase 3 — PORTFOLIO
Module 1 — Constrained Cointegration
Module 2 — Cardinality & Small-Basket Engineering
Module 3 — Direct Mean-Reverting Portfolio Optimisation
Phase 4 — ECONOMICS
Module 1 — Mean-Reversion Characterisation
Module 2 — Volatility Paradox & Variance Floors
Module 3 — Economic Opportunity Mapping
Phase 5 — DYNAMICS
Module 1 — Basket Stability
Module 2 — Temporal Regularisation & Turnover
Module 3 — Dynamic Basket Tracking
Phase 6 — SCIENCE
Module 1 — Combinatorial Search & Candidate Generation
Module 2 — Multiple Testing & False Discovery
Module 3 — Multi-Asset Discovery Laboratory
Special module — Strict Multicointegration (Granger–Lee)
Capstone — Multi-Asset Relationship Discovery Engine
Course content is Phase → Module → Chapter using HARMONIA's six phases (SYSTEM → DISCOVERY → PORTFOLIO → ECONOMICS → DYNAMICS → SCIENCE). Module numbers restart inside each phase. Granger–Lee is a special module, not in the 18. The capstone sits outside the six phases. Lecture bodies are not authored yet. Recommended prerequisite: ARGOS.
Instructor
Elmer Niño
Founder, VTAlgo Group · Systems Engineer · MSc in Computer Science
Algorithmic trader since 2009, running trading as an enterprise. Methodology built on walk-forward analysis, genetic optimization, PCA against over-optimization, the Triple Barrier Method, and 9–12 month live validation before capital.
HARMONIA
Cointegración multi-activo e ingeniería de baskets mean-reverting
Cointegración multi-activo e ingeniería de baskets mean-reverting
$1,800
Misión y visión
Misión
Enseñar el descubrimiento de relaciones multivariadas entre tres o más activos: espacios cointegrantes, baskets ralos y portfolios mean-reverting que puedan defenderse estadística, temporal y económicamente.
Visión
Investigadores que extraen baskets pequeños e interpretables de un espacio de relaciones — no un spread de par, y no la multicointegración estricta de Granger–Lee.
Por qué HARMONIA
HARMONIA es Cointegración multi-activo e ingeniería de baskets mean-reverting.
El wordmark es la armonía entre muchas partes: un espacio cointegrante convertido en un basket pequeño. No significa la multicointegración estricta de Granger–Lee (acumulaciones I(2) de errores de equilibrio). Esa distinción es un módulo especial.
El objeto es `X_t = (A_1, …, A_N)` y `z_t = w' X_t` — relaciones que pueden no ser visibles par a par, convertidas en baskets pequeños. No son las etapas retiradas de TAC (cointegration · failure · relations). No es Forex como identidad. No es el camino de pares de dos activos.
A quién va dirigido
Quantitative researchers, traders sistemáticos, desarrolladores de statistical arbitrage e ingenieros financieros que ya dominan cointegración bivariada (ARGOS o equivalente). Se asumen álgebra lineal, series temporales, ADF y construcción de spreads.
Qué no es
No es ARGOS (pares de dos activos). No es Granger–Lee. No es una receta de cinco nombres. Los cuerpos de lección todavía no están escritos.
Lo que vas a poder hacer
- Pasar de (A, B) → spread a z = w'X sobre tres o más activos
- Estimar el rango de cointegración y un espacio cointegrante — no un basket único
- Extraer vectores ralos, restringidos y operables de ese espacio
- Comparar descubrimiento Econometric-First con Objective-First (MRP directo)
- Validar procedimientos generadores bajo estabilidad, costes, multiplicidad y OOS causal
Contenido del curso
Phase 1 — SYSTEM
Module 1 — From Pair to Multi-Asset System
Module 2 — Johansen & VECM
Module 3 — Cointegrating Spaces
Phase 2 — DISCOVERY
Module 1 — From Cointegrating Space to Tradable Basket
Module 2 — Sparse Cointegration
Module 3 — High-Dimensional Relationship Selection
Phase 3 — PORTFOLIO
Module 1 — Constrained Cointegration
Module 2 — Cardinality & Small-Basket Engineering
Module 3 — Direct Mean-Reverting Portfolio Optimisation
Phase 4 — ECONOMICS
Module 1 — Mean-Reversion Characterisation
Module 2 — Volatility Paradox & Variance Floors
Module 3 — Economic Opportunity Mapping
Phase 5 — DYNAMICS
Module 1 — Basket Stability
Module 2 — Temporal Regularisation & Turnover
Module 3 — Dynamic Basket Tracking
Phase 6 — SCIENCE
Module 1 — Combinatorial Search & Candidate Generation
Module 2 — Multiple Testing & False Discovery
Module 3 — Multi-Asset Discovery Laboratory
Special module — Strict Multicointegration (Granger–Lee)
Capstone — Multi-Asset Relationship Discovery Engine
Course content is Phase → Module → Chapter using HARMONIA's six phases (SYSTEM → DISCOVERY → PORTFOLIO → ECONOMICS → DYNAMICS → SCIENCE). Module numbers restart inside each phase. Granger–Lee is a special module, not in the 18. The capstone sits outside the six phases. Lecture bodies are not authored yet. Recommended prerequisite: ARGOS.
Instructor
Elmer Niño
Fundador, VTAlgo Group · Ingeniero de sistemas · MSc en Ciencias de la Computación
Trader algorítmico desde 2009, operando el trading como empresa. Metodología construida sobre walk-forward, optimización genética, PCA contra el sobreajuste, el Triple Barrier Method, y 9–12 meses de validación en vivo antes de capital.