*! version 1.0.0 21may2026
help mixi12_egh (Stata)

Title

mixi12_egh -- Engsted-Gonzalo-Haldrup (1997) one-step
residual ADF test of multicointegration (delegates to
multicoint, test(egh))

Syntax

mixi12_egh y_flow x_flowlist [if] [in] [, options]

est(name) cointegrating-regression 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

ADF t-test applied to the residual of the single multicointegration
regression

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

where Y_t = Σy_s and X_t = Σx_s. Critical values
follow Engsted-Gonzalo-Haldrup (1997, Tables 1–2) and are interpolated
in the sample size T. Use mixi12_gl for the older two-step
variant.

Stored results

r(t) EGH t-statistic; r(cv01), r(cv025),
r(cv05), r(cv10) critical values; r(lags) lag used;
r(verdict) highest rejection level reached.

Examples

1. Default OLS-based EGH test

mixi12_egh y x, trend(c)

2. Use the TAOLS regression in stage 1

mixi12_egh y x, est(taols) trend(ct)

Author

Dr Merwan Roudane,
merwanroudane920@gmail.com.

Package

Master: mixi12.
Multicointegration commands: mixi12_mco, mixi12_gl,
mixi12_mco_compare.
Engine: multicoint.