*! version 1.0.1 16may2026

Title

ralsfadf -- RALS-Fourier ADF unit-root test (Yilanci, Aydin & Aydin 2019)

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

Syntax

ralsfadf varname [if] [in] [,
trend
maxlags(#)
ic(string)
fmax(#)
frequency(#)
graph
noheader]

Description

ralsfadf estimates the Residual-Augmented Fourier ADF unit-root
regression of Yilanci, Aydin & Aydin (2019),

Dy_t = rho*y_ + c_1 + c_2*t + c_3*sin(2*pi*k*t/T) + c_4*cos(2*pi*k*t/T) + c_5*w_t + v_t

following Enders & Lee (2012a)'s Fourier ADF augmented by the RALS w-vector
(Im & Schmidt 2008). The optimal frequency k is chosen on the grid
1..fmax as the one minimising the OLS sum of squared residuals; the chosen
lag length is reported in r(lag).

Critical values are read from the n x k x rho^2 x percentile table in
Yilanci, Aydin & Aydin (2019, MPRA 96797; Tables 1a & 1b). Linear
interpolation is used both in rho^2 (10-row grid) and in T (5-row grid).

Options

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

maxlags(#) largest Dy_ lag considered (default 8).

ic(string) aic | bic | tstat (default).

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

frequency(#) fix the Fourier frequency (skips the grid search).

graph plots the series with the fitted Fourier component overlaid.

noheader suppresses the header.

Examples

. ralsfadf close, trend graph

. ralsfadf forestfp, trend fmax(3) ic(aic)

Stored results

r(tauFADF) stage-1 Fourier-ADF statistic

r(tauRALS) RALS-FADF statistic

r(rho2) estimated rho^2

r(kfreq) selected Fourier frequency

r(ssr) minimum SSR over the k-grid

r(lag) selected lag length

r(cv01_FADF), r(cv05_FADF), r(cv10_FADF) stage-1 critical values

r(cv01), r(cv05), r(cv10) stage-2 RALS critical values

References

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

Enders, W., Lee, J. (2012a). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters 117(1): 196-199.

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