*! version 1.0.0 03jul2026

Title

tsadvroot -- Advanced time-series unit-root tests: quantile ADF,
Fourier quantile ADF, two-break ADF, and GLS tests with multiple structural
breaks

Syntax

tsadvroot subcommand varname [if] [in] [, options]

where subcommand is one of

qadf quantile ADF unit-root test
(Koenker and Xiao 2004)

fqadf Fourier quantile ADF test with smooth
structural changes (Li and Zheng 2018), with residual bootstrap

npadf unit-root test with two structural breaks
at unknown dates (Narayan and Popp 2010)

cisur GLS-based Pt, MPt, ADF, Za, MZa, MSB and
MZt tests with multiple structural breaks
(Carrion-i-Silvestre, Kim and Perron 2009)

The data must be tsset (a single time series, no gaps in the
estimation sample). Each subcommand has its own help page with the full
syntax, methods, stored results and examples; click the links above.

Description

tsadvroot is a library of modern univariate unit-root tests that go
beyond the classical Dickey-Fuller framework in two directions:

1. Quantile-based testing. The qadf and
fqadf subcommands test the unit-root hypothesis
across the conditional quantiles of the series, so that persistence may
differ in the lower, central and upper parts of the conditional
distribution. fqadf additionally allows smooth structural changes of
unknown form through a flexible Fourier component.

2. Structural breaks. The npadf subcommand
allows two sharp breaks at unknown dates (in the level, or in the level and
slope), and cisur implements the full
Carrion-i-Silvestre, Kim and Perron (2009) battery of quasi-GLS-detrended
tests with up to 3 estimated (or 5 known) breaks, with critical values from
the authors' response surfaces.

All subcommands produce journal-style result tables, optional
publication-quality graphs (graph option), and full r() results
for post-processing.

Subcommands at a glance

Test H0 Breaks Inference

qadf Koenker-Xiao t_n(tau) unit root none Hansen (1995) cv
fqadf Li-Zheng Fourier t_n(tau) unit root smooth bootstrap cv, p
npadf Narayan-Popp ADF unit root 2 sharp NP Table 3 cv
cisur CiS-Kim-Perron 7 tests unit root 0-5 response surfaces

Source compatibility

Each routine is an exact translation of the reference GAUSS source code:

qadf: qr_adf.src (tspdlib, Saban Nazlioglu), procedure
QRADF with the ADF lag pre-selection.

fqadf: qr_fourier_adf.src (tspdlib), procedures
QR_Fourier_ADF and QR_Fourier_ADF_bootstrap.

npadf: narayan pop.src (tspdlib), procedure
ADF_2breaks.

cisur: carrion silvestre2009.src
(Carrion-i-Silvestre, based on Ng-Perron code), procedures sbur_gls
and __sbur_multiple_gls_brute with the response surfaces
__sbur_c_bar_rs and pd_msbur_rsf.

Every numeric convention of the sources is reproduced, including their
idiosyncrasies (documented in the "Source compatibility" section of each
subcommand's help page). Quantile regressions are computed with Stata's
exact qreg solver, which minimizes the same check-function objective
as the GAUSS quantileFit routine; remaining differences are of
numerical-convergence order only.

Examples

. webuse air2, clear

. gen lair = ln(air)

Quantile ADF over the deciles, with the journal-style profile plot

. tsadvroot qadf lair, model(ct) graph

Fourier quantile ADF at the median with 500 bootstrap replications

. tsadvroot fqadf lair, tau(0.5) model(ct) freq(1) nboot(500) seed(12345)

Narayan-Popp two-break test (breaks in level and slope)

. tsadvroot npadf lair, model(2) graph

Carrion-i-Silvestre et al. with two estimated level-and-slope breaks

. tsadvroot cisur lair, model(break) breaks(2) graph

References

Carrion-i-Silvestre, J. L., D. Kim, and P. Perron. 2009. GLS-based unit root
tests with multiple structural breaks under both the null and the
alternative hypotheses. Econometric Theory 25: 1754-1792.

Hansen, B. E. 1995. Rethinking the univariate approach to unit root testing:
Using covariates to increase power. Econometric Theory 11: 1148-1171.

Koenker, R., and Z. Xiao. 2004. Unit root quantile autoregression inference.
Journal of the American Statistical Association 99: 775-787.

Li, H., and C. Zheng. 2018. Unit root quantile autoregression testing with
smooth structural changes. Finance Research Letters 25: 83-89.

Narayan, P. K., and S. Popp. 2010. A new unit root test with two structural
breaks in level and slope at unknown time.
Journal of Applied Statistics 37: 1425-1438.

Ng, S., and P. Perron. 2001. Lag length selection and the construction of
unit root tests with good size and power. Econometrica 69: 1519-1554.

Acknowledgment. The Stata implementation follows the GAUSS routines by
Saban Nazlioglu (tspdlib) and by Josep Lluis Carrion-i-Silvestre (in turn
based on code by Serena Ng and Pierre Perron).

Author

Merwan Roudane

merwanroudane920@gmail.com

https://github.com/merwanroudane

Also see

Help: tsadvroot_qadf, tsadvroot_fqadf,
tsadvroot_npadf, tsadvroot_cisur,
dfuller, dfgls, qreg