*! version 1.0.0 21may2026
help mixi12_mco (Stata)

Title

mixi12_mco -- Multicointegration in the I(1) flow / I(2)
stock setting (delegates to multicoint)

Syntax

mixi12_mco y_flow x_flowlist [if] [in] [, options]

est(name) ols, fmols, dols, ccr, imols, taols (default)

test(name) gl, egh, taols, all (default)

trend(spec) none, c (default), ct, ctt

noconstant suppress the intercept

lags(#) fixed ADF lag (0 = use autolag)

autolag(crit) bic (default), aic, hqic, fixed

maxlags(#) cap on auto-selected lag (default 8)

leads(#) DOLS / TAOLS lead order (default 2)

dlags(#) DOLS / TAOLS lag order (default 2)

kernel(name) bartlett (default), parzen, qs

bwidth(#) HAC bandwidth (0 = Andrews)

k(#) TAOLS basis dimension (default 12)

level(#) confidence level (default 95)

graph produce diagnostic plot afterwards

grsave(file) export the plot

notable suppress estimator/test tables (silent mode)

Description

Multicointegration is the special I(1)/I(2) case in which the I(2)
variables are not directly observed but built as cumulants of underlying
I(1) flows. The actual regression run is

Y_t = α + δ_1·t + δ_2·t² + β'·X_t + γ'·x_t + u_t

with Y_t = Σ y_s and X_t = Σ x_s both I(2), x_t
the original I(1) flows, and u_t ~ I(0) under multicointegration.
Production–sales–inventory (Granger & Lee 1989) and consumption–
income–wealth (Engsted & Haldrup 1999) are the canonical examples.

This command is a thin wrapper around the user's multicoint
package (Roudane 2026), which implements all six estimators (OLS,
FM-OLS, DOLS, CCR, IM-OLS, TAOLS) and all three multicointegration tests
(Granger-Lee 1989/1990, Engsted-Gonzalo-Haldrup 1997, Sun et al. 2026
adaptive F). Use mixi12_mco when you want to keep the analysis
inside the mixi12 narrative; use multicoint directly when you
need the full option surface.

When to choose this over the other mixi12 sub-commands

- mixi12_johansen - your I(2) variables are observed in levels,
e.g. nominal money, prices, monetary base. Estimates two reduced ranks
on the levels VAR. This is the Juselius / Kurita / Majsterek route.

- mixi12_mco - your I(2) variables are constructed as cumulants
of I(1) flows (sales -> inventory; investment -> capital stock). This is
the Granger-Lee / Engsted-Haldrup route.

Stored results

Forwarded from multicoint; see multicoint.

Examples

1. Adaptive Sun et al. TAOLS test (all-in-one)

mixi12_mco y x, est(taols) test(all) trend(c)

2. FM-OLS estimation with EGH one-step test

mixi12_mco y x, est(fmols) test(egh) trend(ct)

3. Classical Granger-Lee two-step ADF

mixi12_mco y x, est(ols) test(gl) trend(c)

Author

Dr Merwan Roudane,
merwanroudane920@gmail.com.

Package

Master: mixi12.
Companions: mixi12_unit, mixi12_haldrup,
mixi12_johansen, mixi12_trans, mixi12_sw,
mixi12_sim, mixi12_graph, mixi12_cv.
Engine: multicoint.