*! version 1.0.1 16may2026

Title

rals -- Residual Augmented Least Squares unit-root and cointegration tests

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Unit-root tests

ralsadf - RALS-ADF

ralslm - RALS-LM

ralslmb - RALS-LM with structural breaks

ralsfadf - RALS-Fourier ADF

ralsfkss - RALS-Fourier KSS

Run-all driver

ralsbattery - run every test in the package on one or more series

Cointegration tests

ralscoint - RALS ECM / ADL / EG / EG2

ralsfadl - RALS-Fourier ADL cointegration

Diagnostics

ralsdiag - Normality, linearity and rho^2 diagnostics

Description

The rals package implements every test in the Residual Augmented
Least Squares family (Im & Schmidt 2008): the second- and third-moment
information in the regression residuals is exploited to gain power whenever
the errors are non-normal. The package collects nine commands covering
both unit-root and cointegration testing, with optional Fourier deterministic
components and structural breaks. All routines reproduce the original GAUSS
code shipped with the source papers (rals_adf.src, rals_lm.src,
rals_lm_breaks.src, RALS_coint_size_power.g, RALS_coint_crit.g) and the
Eviews routines ralsfadl1..4.prg used in Yilanci et al. (2022).

Author: Dr Merwan Roudane, merwanroudane920@gmail.com

Quick start

. sysuse sp500, clear

. gen t = _n

. tsset t

. ralsdiag close, trend

. ralsadf close, trend graph

. ralsbattery close volume open, trend graph // run all tests on all variables

References

Im, K.S., Schmidt, P. (2008). More efficient estimation under non-normality when higher moments do not depend on the regressors, using residual augmented least squares. Journal of Econometrics 144(1): 219-233.

Im, K.S., Lee, J., Tieslau, M.A. (2014). More powerful unit root tests with non-normal errors. Festschrift in Honor of Peter Schmidt, 315-342.

Meng, M., Im, K.S., Lee, J., Tieslau, M.A. (2014). More powerful LM unit root tests with non-normal errors. Festschrift, 343-357.

Meng, M., Lee, J., Payne, J.E. (2017). RALS-LM unit root test with trend breaks and non-normal errors. Studies in Nonlinear Dynamics & Econometrics 21(1): 31-45.

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

Yilanci, V., Aydin, M., Aydin, M. (2019). Residual Augmented Fourier ADF Unit Root Test. MPRA Paper No. 96797.

Yilanci, V., Ulucak, R., Zhang, Y., Andreoni, V. (2022). The role of affluence, urbanization and human capital for sustainable forest management in China. Sustainable Development 31(2): 812-824.

Yilanci, V., Ozgur, O. (2025). Testing Real Interest Rate Parity for EU5 Countries. Politicka Ekonomie 73(3): 528-565.

Author

Dr Merwan Roudane -- merwanroudane920@gmail.com

Version 1.0.1 -- 16 May 2026