*! version 1.0.0 21may2026
help mixi12_gl (Stata)

Title

mixi12_gl -- Granger-Lee (1989, 1990) two-step
multicointegration test (delegates to multicoint, test(gl))

Syntax

mixi12_gl y_flow x_flowlist [if] [in] [, options]

est(name) stage-1 estimator: ols (default), fmols, dols, ccr, imols, taols

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

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

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

leads(#) lead order (default 2)

dlags(#) lag order (default 2)

kernel(name) bartlett, parzen, qs

k(#) TAOLS basis dimension (default 12)

level(#) confidence level (default 95)

Description

The original multicointegration test of Granger & Lee (1989, JAE; 1990,
Advances in Econometrics 8). Two stages:

1. Regress y_t on x_t and save residual Z_t.

2. Cumulate Z_t into S_t = ΣZ_s, regress S_t on
x_t and apply an ADF test to the stage-2 residual.

Rejection of the unit-root null supports multicointegration.

Stored results

r(stat) GL statistic, r(cv05) 5% critical value,
r(verdict) reject / do-not-reject sentence.

Examples

1. Default OLS-based GL test

mixi12_gl y x, trend(c)

2. Use FM-OLS in stage 1

mixi12_gl y x, est(fmols) trend(ct)

Author

Dr Merwan Roudane,
merwanroudane920@gmail.com.

Package

Master: mixi12.
Multicointegration commands: mixi12_mco, mixi12_egh,
mixi12_mco_compare.
Engine: multicoint.