*! version 1.0.1 16may2026

Title

ralscoint -- RALS cointegration tests (ECM / ADL / EG / EG2)

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Overview |
adf |
lm |
lm-breaks |
f-adf |
f-kss |
battery |
coint |
f-adl |
diag

Syntax

ralscoint depvar regressors [if] [in] [,
trend
method(string)
beta(#)
bw(#)
graph
noheader]

depvar is the LHS I(1) series; regressors are one or more I(1)
explanatory series. tsset must be active.

Description

ralscoint runs the four single-equation cointegration tests of Lee,
Lee & Im (2015) -- error-correction (ECM), augmented distributed lag (ADL),
Engle-Granger (EG) and the modified EG2 of Lee (2012) -- in both their
standard OLS form and in the Residual-Augmented Least-Squares (RALS) version
that augments each regression with

w_t = (e_t^2 - m_2, e_t^3 - m_3 - 3*m_2*e_t)'.

The nuisance parameter rho^2 driving the limiting distribution is computed
via Newey-West long-run variances exactly as in RALS_coint_size_power.g.
Critical values are taken from the embedded tables of the GAUSS supplement
and interpolated across rho^2.

Options

trend include a linear trend (model 2). Default model 1.

method(string) ecm | adl | eg | eg2 | all (default).

beta(#) pre-specified cointegration coefficient used by the ECM test (default 1).

bw(#) bandwidth for the LR variance kernel (0 = automatic).

graph draws a 2-line plot of depvar against the first regressor.

noheader suppresses the header.

Examples

. tsset year

. ralscoint y x1 x2, trend

. ralscoint forestfp gdp_pc urban hc tfp, trend graph

Stored results

r(ECM_t) ... r(EG2_t) stage-1 OLS test statistics

r(ECM_rals) ... r(EG2_rals) RALS statistics

r(ECM_rho2) ... r(EG2_rho2) estimated rho^2 for each test

r(cv) 4x4 matrix: (OLS-5%, RALS-1%, RALS-5%, RALS-10%) per test

r(T) sample size

References

Lee, H., Lee, J., Im, K. (2015). More powerful cointegration tests with non-normal errors. SNDE 19(4): 397-413.

Lee, H. (2012). Three essays on more powerful cointegration tests. PhD dissertation, University of Alabama.

See also

Back to overview: rals

Unit-root tests: ralsadf, ralslm, ralslmb, ralsfadf, ralsfkss

Battery (run-all): ralsbattery

Cointegration tests: ralscoint, ralsfadl

Diagnostics: ralsdiag

Author

Dr Merwan Roudane -- merwanroudane920@gmail.com