*! version 1.0.1 16may2026

Title

ralsfadl -- RALS-Fourier ADL cointegration test (Yilanci, Ulucak, Zhang & Andreoni 2022)

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

Syntax

ralsfadl depvar regressors [if] [in] [,
trend
maxlags(#)
fmax(#)
frequency(#)
graph
noheader]

depvar is the dependent series; up to four explanatory series may be
supplied (matching the four Eviews scripts ralsfadl1..4.prg from the source
paper). tsset must be active.

Description

ralsfadl fits the Fourier-augmented ADL cointegration regression of
Banerjee, Arcabic & Lee (2017),

Dy_t = b_0 + b_1*sin(2*pi*k*t/T) + b_2*cos(2*pi*k*t/T) + d_1*y_ + g'*x_ + a'*Dx_t + sum Dy_ + eps_t,

and augments it with the RALS w-terms (Im & Schmidt 2008; Lee et al. 2015)
to obtain the RALS-FADL statistic. Both the Fourier frequency k and
the lag of Dy_t are chosen jointly to minimise the AIC, exactly as in the
Eviews loop of the supplement. Critical values come from Tables A1-A2 of
Yilanci et al. (2022) and are interpolated across rho^2 and sample size.

Options

trend adds a deterministic trend. Default constant-only.

maxlags(#) largest lag of Dy_ (default 3, matching the Eviews code).

fmax(#) largest Fourier frequency searched (default 5).

frequency(#) fix the frequency at a known integer.

graph plots depvar and the first regressor with the Fourier component.

noheader suppresses the header.

Examples

. tsset year

. ralsfadl forestfp gdp urb hc tfp, trend graph

. ralsfadl co2pc ecpc, fmax(3)

Stored results

r(tauFADL) Fourier-ADL statistic (stage 1)

r(tauRALS) RALS-FADL statistic

r(rho2) estimated rho^2

r(kfreq) optimal Fourier frequency

r(lag) selected Dy lag

r(AIC) minimum AIC across the k x p grid

r(cv01), r(cv05), r(cv10) critical values at the estimated rho^2

References

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.

Banerjee, A., Arcabic, V., Lee, H. (2017). Fourier ADL cointegration test. Economic Modelling 67: 114-124.

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