*! version 1.0.1 16may2026

Title

ralsfkss -- RALS-Fourier KSS unit-root test (Yilanci & Ozgur 2025)

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

Syntax

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

Description

ralsfkss implements the RALS-Fourier KSS unit-root test of Yilanci &
Ozgur (2025). The series is first de-trended with a Fourier function
(Christopoulos & Leon-Ledesma 2010); the de-trended residuals u_t are then
plugged into a Kapetanios-Shin-Snell (KSS) regression

Du_t = phi_1 * u^3_ + sum zeta_i Du_ + e_t,

and finally the second-stage residuals are augmented with the RALS w-vector
to gain power under non-normal innovations.

Options

trend adds a linear trend in the de-trending stage.

maxlags(#) largest Du_ lag (default 8).

ic(string) aic (default), bic or tstat.

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

frequency(#) fix the Fourier frequency directly.

graph time-series plot with the chosen Fourier component overlaid.

noheader suppress the header.

Examples

. ralsfkss close, trend graph

. ralsfkss rid_italy, fmax(3)

Stored results

r(tauKSS) stage-1 KSS statistic

r(tauRALS) RALS-FKSS statistic

r(rho2) estimated rho^2

r(kfreq) selected Fourier frequency

r(lag) selected lag length

r(cv01_FKSS), r(cv05_FKSS), r(cv10_FKSS) stage-1 critical values

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

References

Yilanci, V., Ozgur, O. (2025). Testing Real Interest Rate Parity for EU5 Countries: 200 Years of Data, Non-normality, Non-linearity and Breaks. Politicka Ekonomie 73(3): 528-565.

Christopoulos, D.K., Leon-Ledesma, M.A. (2010). Smooth breaks and non-linear mean reversion. Journal of International Money and Finance 29(6): 1076-1093.

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